Signal processing apparatus

ABSTRACT

A signal processor which acquires a first signal, including a first primary signal portion and a first secondary signal portion, and a second signal, including a second primary signal portion and a second secondary signal portion, wherein the first and second primary signal portions are correlated. The signals may be acquired by propagating energy through a medium and measuring an attenuated signal after transmission or reflection. Alternatively, the signals may be acquired by measuring energy generated by the medium. A processor of the present invention generates a primary or secondary reference signal which is a combination, respectively, of only the primary or secondary signal portions. The secondary reference signal is then used to remove the secondary portion of each of the first and second measured signals via a correlation canceler, such as an adaptive noise canceler, preferably of the joint process estimator type. The primary reference signal is used to remove the primary portion of each of the first and second measured signals via a correlation canceler. The processor of the present invention may be employed in conjunction with a correlation canceler in physiological monitors wherein the known properties of energy attenuation through a medium are used to determine physiological characteristics of the medium. Many physiological conditions, such as the pulse, or blood pressure of a patient or the concentration of a constituent in a medium, can be determined from the primary or secondary portions of the signal after other signal portion is removed.

PRIORITY CLAIM

This application is a continuation of U.S. patent application Ser. No.10/779,033, filed Feb. 13, 2004, which is a continuation of U.S. patentapplication Ser. No. 09/111,604, filed Jul. 7, 1998, which is acontinuation of U.S. patent application Ser. No. 08/943,511, filed Oct.6, 1997, now U.S. Pat. No. 6,263,222, which is a continuation of U.S.patent application Ser. No. 08/572,488, filed Dec. 14, 1995, now U.S.Pat. No. 5,685,299, which is a continuation of U.S. application Ser. No.08/132,812, filed on Oct. 6, 1993, now U.S. Pat. No. 5,490,505, which isa continuation-in-part of U.S. patent application Ser. No. 07/666,060,filed Mar. 7, 1991, now abandoned. The present application incorporateseach of the foregoing disclosures herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to the field of signal processing. Morespecifically, the present invention relates to the processing ofmeasured signals, containing a primary and a secondary signal, for theremoval or derivation of either the primary or secondary signal whenlittle is known about either of these components. The present inventionalso relates to the use of a novel processor which in conjunction with acorrelation canceler, such as an adaptive noise canceler, producesprimary and/or secondary signals. The present invention is especiallyuseful for physiological monitoring systems including blood oxygensaturation.

2. Description of the Related Art

Signal processors are typically employed to remove or derive either theprimary or secondary signal portion from a composite measured signalincluding a primary signal portion and a secondary signal portion. Ifthe secondary signal portion occupies a different frequency spectrumthan the primary signal portion, then conventional filtering techniquessuch as low pass, band pass, and high pass filtering could be used toremove or derive either the primary or the secondary signal portion fromthe total signal. Fixed single or multiple notch filters could also beemployed if the primary and/or secondary signal portion(s) exit at afixed frequency(s).

It is often the case that an overlap in frequency spectrum between theprimary and secondary signal portions exists. Complicating mattersfurther, the statistical properties of one or both of the primary andsecondary signal portions change with time. In such cases, conventionalfiltering techniques are totally ineffective in extracting either theprimary or secondary signal. If, however, a description of either theprimary or secondary signal portion can be made available correlationcanceling, such as adaptive noise canceling, can be employed to removeeither the primary or secondary signal portion of the signal leaving theother portion available for measurement.

Correlation cancelers, such as adaptive noise cancelers, dynamicallychange their transfer function to adapt to and remove either the primaryor secondary signal portions of a composite signal. Correlationcancelers require either a secondary reference or a primary referencewhich is correlated to either the secondary signal or the primary signalportions only. The reference signals are not necessarily arepresentation of the primary or secondary signal portions, but have afrequency spectrum which is similar to that of the primary or secondarysignal portions. In many cases, it requires considerable ingenuity todetermine a reference signal since nothing is usually known a prioriabout the secondary and/or primary signal portions.

One area where composite measured signals comprising a primary signalportion and a secondary signal portion about which no information caneasily be determined is physiological monitoring. Physiologicalmonitoring apparatuses generally measure signals derived from aphysiological system, such as the human body. Measurements which aretypically taken with physiological monitoring systems includeelectrocardiographs, blood pressure, blood gas saturation (such asoxygen saturation), capnographs, heart rate, respiration rate, and depthof anesthesia, for example. Other types of measurements include thosewhich measure the pressure and quantity of a substance within the bodysuch as breathalyzer testing, drug testing, cholesterol testing, glucosetesting, arterial carbon dioxide testing, protein testing, and carbonmonoxide testing, for example. Complications arising in thesemeasurements are often due to motion of the patient, both external andinternal (muscle movement, for example), during the measurement process.

Knowledge of physiological systems, such as the amount of oxygen in apatient's blood, can be critical, for example during surgery. These datacan be determined by a lengthy invasive procedure of extracting andtesting matter, such as blood, from a patient, or by more expedient,non-invasive measures. Many types of non-invasive measurements can bemade by using the known properties of energy attenuation as a selectedform of energy passes through a medium.

Energy is caused to be incident on a medium either derived from orcontained within a patient and the amplitude of transmitted or reflectedenergy is then measured. The amount of attenuation of the incidentenergy caused by the medium is strongly dependent on the thickness andcomposition of the medium through which the energy must pass as well asthe specific form of energy selected. Information about a physiologicalsystem can be derived from data taken from the attenuated signal of theincident energy transmitted through the medium if either the primary orsecondary signal of the composite measurement signal can be removed.However, non-invasive measurements often do not afford the opportunityto selectively observe the interference causing either the primary orsecondary signal portions, making it difficult to extract either one ofthem from the composite signal.

The primary and/or secondary signal portions often originate from bothAC and/or DC sources. The DC portions are caused by transmission of theenergy through differing media which are of relatively constantthickness within the body, such as bone, tissue, skin, blood, etc. Theseportions are easy to remove from a composite signal. The AC componentsare caused by physiological pulsations or when differing media beingmeasured are perturbed and thus, change in thickness while themeasurement is being made. Since most materials in and derived from thebody are easily compressed, the thickness of such matter changes if thepatient moves during a non-invasive physiological measurement. Patientmovement, muscular movement and vessel movement, can cause theproperties of energy attenuation to vary erratically. Traditional signalfiltering techniques are frequently totally ineffective and grosslydeficient in removing these motion induced effects from a signal. Theerratic or unpredictable nature of motion induced signal components isthe major obstacle in removing or deriving them. Thus, presentlyavailable physiological monitors generally become totally inoperativeduring time periods when the measurement site is perturbed.

A blood gas monitor is one example of a physiological monitoring systemwhich is based upon the measurement of energy attenuated by biologicaltissues or substances. Blood gas monitors transmit light into the tissueand measure the attenuation of the light as a function of time. Theoutput signal of a blood gas monitor which is sensitive to the arterialblood flow contains a component which is a waveform representative ofthe patient's arterial pulse. This type of signal, which contains acomponent related to the patient's pulse, is called a plethysmographicwave, and is shown in FIG. 1 as curve s. Plethysmographic waveforms areused in blood pressure or blood gas saturation measurements, forexample. As the heart beats, the amount of blood in the arteriesincreases and decreases, causing increases and decreases in energyattenuation, illustrated by the cyclic waves in FIG. 1.

Typically, a digit such as a finger, an ear lobe, or other portion ofthe body where blood flows close to the skin, is employed as the mediumthrough which light energy is transmitted for blood gas attenuationmeasurements. The finger comprises skin, fat, bone, muscle, etc., shownschematically in FIG. 2, each of which attenuates energy incident on thefinger in a generally predictable and constant manner. However, whenfleshy portions of the finger are compressed erratically, for example bymotion of the finger, energy attenuation becomes erratic.

An example of a more realistic measured waveform S is shown in FIG. 3,illustrating the effect of motion. The primary plethysmographic waveformportion of the signal s is the waveform representative of the pulse,corresponding to the sawtooth-like pattern wave in FIG. 1. The large,secondary motion-induced excursions in signal amplitude hide the primaryplethysmographic signal s. It is easy to see how even small variationsin amplitude make it difficult to distinguish the primary signal s inthe presence of a secondary signal component n.

A specific example of a blood gas monitoring apparatus is a pulseoximeter which measures the arterial saturation of oxygen in the blood.The pumping of the heart forces freshly oxygenated blood into thearteries causing greater energy attenuation. The arterial saturation ofoxygenated blood may be determined from the depth of the valleysrelative to the peaks of two plethysmographic waveforms measured atseparate wavelengths. Patient movement introduces signal portions mostlydue to venous blood, or motion artifacts, to the plethysmographicwaveform illustrated in FIG. 3. It is these motion artifacts which mustbe removed from the measured signal for the oximeter to continue themeasurement of arterial blood oxygen saturation, even during periodswhen the patient moves. It is also these motion artifacts which must bederived from the measured signal for the oximeter to obtain an estimateof venous blood oxygen saturation. Once the signal components due toeither arterial blood or venous blood is known, its corresponding oxygensaturation may be determined.

SUMMARY OF THE INVENTION

This invention is an improvement of U.S. patent application Ser. No.07/666,060 filed Mar. 7, 1991 and entitled Signal Processing Apparatusand Method, which earlier application has been assigned to the assigneeof the instant application. The invention is a signal processor whichacquires a first signal and a second signal that is correlated to thefirst signal. The first signal comprises a first primary signal portionand a first secondary signal portion. The second signal comprises asecond primary signal portion and a second secondary signal portion. Thesignals may be acquired by propagating energy through a medium andmeasuring an attenuated signal after transmission or reflection.Alternatively, the signals may be acquired by measuring energy generatedby the medium.

The first and second measured signals are processed to generate asecondary reference which does not contain the primary signal portionsfrom either of the first or second measured signals. The remainingsecondary signal portions from the first and second measured signals arecombined to form the secondary reference. This secondary reference iscorrelated to the secondary signal portion of each of the first andsecond measured signals.

The secondary reference is then used to remove the secondary portion ofeach of the first and second measured signals via a correlationcanceler, such as an adaptive noise canceler. The correlation canceleris a device which takes a first and second input and removes from thefirst input all signal components which are correlated to the secondinput. Any unit which performs or nearly performs this function isherein considered to be a correlation canceler. An adaptive correlationcanceler can be described by analogy to a dynamic multiple notch filterwhich dynamically changes its transfer function in response to areference signal and the measured signals to remove frequencies from themeasured signals that are also present in the reference signal. Thus, atypical adaptive correlation canceler receives the signal from which itis desired to remove a component and a reference signal. The output ofthe correlation canceler is a good approximation to the desired signalwith the undesired component removed.

Alternatively, the first and second measured signals may be processed togenerate a primary reference which does not contain the secondary signalportions from either of the first or second measured signals. Theremaining primary signal portions from the first and second measuredsignals are combined to form the primary reference. The primaryreference may then be used to remove the primary portion of each of thefirst and second measured signals via a correlation canceler. The outputof the correlation canceler is a good approximation to the secondarysignal with the primary signal removed and may be used for subsequentprocessing in the same instrument or an auxiliary instrument. In thiscapacity, the approximation to the secondary signal may be used as areference signal for input to a second correlation canceler togetherwith either the first or second measured signals for computation of,respectively, either the first or second primary signal portions.

Physiological monitors can often advantageously employ signal processorsof the present invention. Often in physiological measurements a firstsignal comprising a first primary portion and a first secondary portionand a second signal comprising a second primary portion and a secondsecondary portion are acquired. The signals may be acquired bypropagating energy through a patient's body (or a material which isderived from the body, such as breath, blood, or tissue, for example) orinside a vessel and measuring an attenuated signal after transmission orreflection. Alternatively, the signal may be acquired by measuringenergy generated by a patient's body, such as in electrocardiography.The signals are processed via the signal processor of the presentinvention to acquire either a secondary reference or a primary referencewhich is input to a correlation canceler, such as an adaptive noisecanceler.

One physiological monitoring apparatus which can advantageouslyincorporate the features of the present invention is a monitoring systemwhich determines a signal which is representative of the arterial pulse,called a plethysmographic wave. This signal can be used in bloodpressure calculations, blood gas saturation measurements, etc. Aspecific example of such a use is in pulse oximetry which determines thesaturation of oxygen in the blood. In this configuration, we define theprimary portion of the signal to be the arterial blood contribution toattenuation of energy as it passes through a portion of the body whereblood flows close to the skin. The pumping of the heart causes bloodflow to increase and decrease in the arteries in a periodic fashion,causing periodic attenuation wherein the periodic waveform is theplethysmographic waveform representative of the arterial pulse. Wedefine the secondary portion of the signal to be that which is usuallyconsidered to be noise. This portion of the signal is related to thevenous blood contribution to attenuation of energy as it passes throughthe body. Patient movement causes this component to flow in anunpredictable manner, causing unpredictable attenuation and corruptingthe otherwise periodic plethysmographic waveform. Respiration alsocauses secondary or noise component to vary, although typically at amuch lower frequency than the patients pulse rate.

A physiological monitor particularly adapted to pulse oximetry oxygensaturation measurement comprises two light emitting diodes (LED's) whichemit light at different wavelengths to produce first and second signals.A detector registers the attenuation of the two different energy signalsafter each passes through an absorptive media, for example a digit suchas a finger, or an earlobe. The attenuated signals generally compriseboth primary and secondary signal portions. A static filtering system,such as a bandpass filter, removes a portion of the secondary signalwhich is outside of a known bandwidth of interest, leaving an erratic orrandom secondary signal portion, often caused by motion and oftendifficult to remove, along with the primary signal portion.

Next, a processor of the present invention removes the primary signalportions from the measured signals yielding a secondary reference whichis a combination of the remaining secondary signal portions. Thesecondary reference is correlated to both of the secondary signalportions. The secondary reference and at least one of the measuredsignals are input to a correlation canceler, such as an adaptive noisecanceler, which removes the random or erratic portion of the secondarysignal. This yields a good approximation to the primary plethysmographicsignal as measured at one of the measured signal wavelengths. As isknown in the art, quantitative measurements of the amount of oxygenatedarterial blood in the body can be determined from the plethysmographicsignal in a variety of ways.

The processor of the present invention may also remove the secondarysignal portions from the measured signals yielding a primary referencewhich is a combination of the remaining primary signal portions. Theprimary reference is correlated to both of the primary signal portions.The primary reference and at least one of the measured signals are inputto a correlation canceler which removes the primary portions of themeasured signals. This yields a good approximation to the secondarysignal at one of the measured signal wavelengths. This signal may beuseful for removing secondary signals from an auxiliary instrument aswell as determining venous blood oxygen saturation.

One aspect of the present invention is a signal processor comprising adetector for receiving a first signal which travels along a firstpropagation path and a second signal which travels along a secondpropagation path wherein a portion of the first and second propagationpaths are located in a propagation medium. The first signal has a firstprimary signal portion and a first secondary signal portion and thesecond signal has a second primary signal portion and a second secondarysignal portion. The first and second secondary signal portions are aresult of a change of the propagation medium. This aspect of theinvention additionally comprises a reference processor having an inputfor receiving the first and second signals. The processor is adapted tocombine the first and second signals to generate a secondary referencehaving a significant component which is a function of the first and saidsecond secondary signal portions. The processor may also be adapted tocombine the first and second signals to generate a primary referencehaving a significant component which is a function of the first andsecond primary signal portions

The above described aspect of the present invention may further comprisea signal processor for receiving the secondary reference signal and thefirst signal and for deriving therefrom an output signal having asignificant component which is a function of the first primary signalportion of the first signal. Alternatively, the above described aspectof the present invention may further comprise a signal processor forreceiving the secondary reference signal and the second signal and forderiving therefrom an output signal having a significant component whichis a function of the second primary signal portion of the second signal.Alternatively, the above described aspect of the present invention mayfurther comprise a signal processor for receiving the primary referenceand the first signal and for deriving therefrom an output signal havinga significant component which is a function of the first secondarysignal portion of the signal of the first signal. Alternatively, theabove described aspect of the present invention may further comprise asignal processor for receiving the primary reference and the secondsignal and for deriving therefrom an output signal having a significantcomponent which is a function of the second secondary signal portion ofthe second signal. The signal processor may comprise a correlationcanceler, such as an adaptive noise canceler. The adaptive noisecanceler may comprise a joint process estimator having aleast-squares-lattice predictor and a regression filter.

The detector in the aspect of the signal processor of the presentinvention described above may further comprise a sensor for sensing aphysiological function. The sensor may comprise a light or otherelectromagnetic sensitive device. Additionally, the present inventionmay further comprise a pulse oximeter for measuring oxygen saturation ina living organism. The present invention may further comprise anelectrocardiograph.

Another aspect of the present invention is a physiological monitoringapparatus comprising a detector for receiving a first physiologicalmeasurement signal which travels along a first propagation path and asecond physiological measurement signal which travels along a secondpropagation path. A portion of the first and second propagation pathsbeing located in the same propagation medium. The first signal has afirst primary signal portion and a first secondary signal portion andthe second signal has a second primary signal portion and a secondsecondary signal portion. The physiological monitoring apparatus furthercomprises a reference processor having an input for receiving the firstand second signals. The processor is adapted to combine the first andsecond signals to generate a secondary reference signal having asignificant component which is a function of the first and the secondsecondary signal portions. Alternatively, the processor may be adaptedto combine the first and second signals to generate a primary referencehaving a component which is a function of the first and second primarysignal portions.

The physiological monitoring apparatus may further comprise a signalprocessor for receiving the secondary reference and the first signal andfor deriving therefrom an output signal having a significant componentwhich is a function of the first primary signal portion of the firstsignal. Alternatively, the physiological monitoring apparatus mayfurther comprise a signal processor for receiving the secondaryreference and the second signal and for deriving therefrom an outputsignal having a significant component which is a function of the secondprimary signal portion of the second signal. Alternatively, thephysiological monitoring apparatus may further comprise a signalprocessor for receiving the primary reference and the first signal andderiving therefrom an output signal having a significant component whichis a function of the first secondary signal portion of the first signal.Alternatively, the physiological monitoring apparatus may furthercomprise a signal processor for receiving the primary reference and thesecond signal and deriving therefrom an output signal having asignificant component which is a function of the second secondary signalportion of the second signal.

A further aspect of the present invention is an apparatus for measuringa blood constituent comprising an energy source for directing aplurality of predetermined wavelengths of electromagnetic energy upon aspecimen and a detector for receiving the plurality of predeterminedwavelengths of electromagnetic energy from the specimen. The detectorproduces electrical signals corresponding to the predeterminedwavelengths in response to the electromagnetic energy. At least two ofthe electrical signals are used each having a primary signal portion andan secondary signal portion. Additionally, the apparatus comprises areference processor having an input for receiving the electricalsignals. The processor is configured to combine said electrical signalsto generate a secondary reference having a significant component whichis derived from the secondary signal portions. Alternatively, theprocessor may be configured to combine said signals to generate aprimary reference having a significant component which is derived fromthe primary signal portions.

This aspect of the present invention may further comprise a signalprocessor for receiving the secondary reference and one of the twoelectrical signals and for deriving therefrom an output signal having asignificant component which is a function of the primary signal portionof one of the two electrical signals. Another aspect of the presentinvention may further comprise a signal processor for receiving theprimary reference and one of the two electrical signals and for derivingtherefrom an output signal having a significant component which is afunction of the secondary signal portion of one of the two electricalsignals. This may be accomplished by use of a correlation canceler, suchas an adaptive noise canceler, in the signal processor which may employa joint process estimator having a least-squares-lattice predictor and aregression filter.

Yet another aspect of the present invention is a blood gas monitor fornon-invasively measuring a blood constituent in a body comprising alight source for directing at least two predetermined wavelengths oflight upon a body and a detector for receiving the light from the body.The detector, in response to the light from the body, produces at leasttwo electrical signals corresponding to the at least two predeterminedwavelengths of light. The at least two electrical signals each have aprimary signal portion and a secondary signal portion. The bloodoximeter further comprises a reference processor having an input forreceiving the at least two electrical signals. The processor is adaptedto combine the at least two electrical signals to generate a secondaryreference with a significant component which is derived from thesecondary signal portions. The blood oximeter may further comprise asignal processor for receiving the secondary reference and the twoelectrical signals and for deriving therefrom at least two outputsignals which are substantially equal, respectively, to the primarysignal portions of the electrical signals. Alternatively, the referenceprocessor may be adapted to combine the at least two electrical signalsto generate a primary reference with a significant component which isderived from the primary signal portions. The blood oximeter may furthercomprise a signal processor for receiving the primary reference and thetwo electrical signals and for deriving therefrom at least two outputsignals which are substantially equivalent to the secondary signalportions of the electrical signal. The signal processor may comprise ajoint process estimator.

The present invention also includes a method of determining a secondaryreference from a first signal comprising a first primary signal portionand a first secondary portion and a second signal comprising a secondprimary signal portion and a second secondary portion. The methodcomprises the steps of selecting a signal coefficient which isproportional to a ratio of predetermined attributes of the first primarysignal portion and predetermined attributes of the second primary signalportion. The first signal and the signal coefficient are input into asignal multiplier wherein the first signal is multiplied by the signalcoefficient thereby generating a first intermediate signal. The secondsignal and the first intermediate signal are input into a signalsubtractor wherein the first intermediate signal is subtracted from thesecond signal. This generates a secondary reference having a significantcomponent which is derived from the first and second secondary signalportions.

The present invention also includes a method of determining a primaryreference from a first signal comprising a first primary signal portionand a first secondary signal portion and a second signal comprising asecond primary signal portion and a second secondary signal portion. Themethod comprises the steps of selecting a signal coefficient which isproportional to a ratio of the predetermined attributes of the firstsecondary signal portion and predetermined attributes of the secondsecondary signal portion. The first signal and the signal coefficientare input into a signal multiplier wherein the first signal ismultiplied by the signal coefficient thereby generating a firstintermediate signal. The second signal and the first intermediate signalare input into a signal subtractor wherein the first intermediate signalis subtracted from the second signal. This generates a primary referencehaving a significant component which is derived from the first andsecond primary signal portions. The first and second signals in thismethod may be derived from electromagnetic energy transmitted through anabsorbing medium.

The present invention further embodies a physiological monitoringapparatus comprising means for acquiring a first signal comprising afirst primary signal portion and a first secondary signal portion and asecond signal comprising a second primary signal portion and a secondsecondary signal portion. The physiological monitoring apparatus of thepresent invention also comprises means for determining from the firstand second signals a secondary reference. Additionally, the monitoringapparatus comprises a correlation canceler, such as an adaptive noisecanceler, having a secondary reference input for receiving the secondaryreference and a signal input for receiving the first signal wherein thecorrelation canceler, in real or near real time, generates an outputsignal which approximates the first primary signal portion.Alternatively, the physiological monitoring device may also comprisemeans for determining from the first and second signals a primaryreference. Additionally, the monitoring apparatus comprises acorrelation canceler having a primary reference input for receiving theprimary reference and a signal input for receiving the first signalwherein the correlation canceler, in real or near real time, generatesan output signal which approximates the first secondary signal portion.The correlation canceler may further comprise a joint process estimator.

A further aspect of the present invention is an apparatus for processingan amplitude modulated signal having a signal amplitude complicatingfeature, the apparatus comprising an energy source for directingelectromagnetic energy upon a specimen. Additionally, the apparatuscomprises a detector for acquiring a first amplitude modulated signaland a second amplitude modulated signal. Each of the first and secondsignals has a component containing information about the attenuation ofelectromagnetic energy by the specimen and a signal amplitudecomplicating feature. The apparatus includes a reference processor forreceiving the first and second amplitude modulated signals and derivingtherefrom a secondary reference which is correlated with the signalamplitude complicating feature. Further, the apparatus incorporates acorrelation canceler having a signal input for receiving the firstamplitude modulated signal, a secondary reference input for receivingthe secondary reference, wherein the correlation canceler produces anoutput signal having a significant component which is derived from thecomponent containing information about the attenuation ofelectromagnetic energy by the specimen. Alternatively, the apparatus mayalso include a reference processor for receiving the first and secondamplitude modulated signals and deriving therefrom a primary referencewhich is correlated with the component containing information about theattenuation of electromagnetic energy by the specimen. Further, theapparatus incorporates a correlation canceler having a signal input forreceiving the first amplitude modulated signal, a primary referenceinput for receiving the primary reference, wherein the correlationcanceler produces an output signal having a primary component which isderived from the signal amplitude complicating feature.

Still another aspect of the present invention is an apparatus forextracting a plethysmographic waveform from an amplitude modulatedsignal having a signal amplitude complicating feature, the apparatuscomprising a light source for transmitting light into an organism and adetector for monitoring light from the organism. The detector produces afirst light attenuation signal and a second light attenuation signal,wherein each of the first and second light attenuation signals has acomponent which is representative of a plethysmographic waveform and acomponent which is representative of the signal amplitude complicatingfeature. The apparatus also includes a reference processor for receivingthe first and second light attenuation signals and deriving therefrom asecondary reference. The secondary reference and the signal amplitudecomplicating feature each have a frequency spectrum. The frequencyspectrum of the secondary reference is correlated with the frequencyspectrum of the signal amplitude complicating feature. Additionallyincorporated into this embodiment of the present invention is acorrelation canceler having a signal input for receiving the firstattenuation signal and a secondary reference input for receiving thesecondary reference. The correlation canceler produces an output signalhaving a significant component which is derived from the component whichis representative of a plethysmographic waveform. The apparatus may alsoinclude a reference processor for receiving the first and second lightattenuation signals and deriving therefrom a primary reference.Additionally incorporated in this embodiment of the present invention isa correlation canceler having a signal input for receiving the firstattenuation signal and a primary reference input for receiving theprimary reference. The correlation canceler produces an output signalhaving a significant component which is derived from the component whichis representative of the signal complicating feature.

The present invention also comprises a method of removing or determininga motion artifact signal from a signal derived from a physiologicalmeasurement wherein a first signal having a physiological measurementcomponent and a motion artifact component and a second signal having aphysiological measurement component and a motion artifact component areacquired. From the first and second signals a secondary reference whichis a primary function of the first and second signals motion artifactcomponents is derived. This method of removing a motion artifact signalfrom a signal derived from a physiological measurement may also comprisethe step of inputting the secondary reference into a correlationcanceler, such as an adaptive noise canceler, to produce an outputsignal which is a significant function of the physiological measurementcomponent of the first or second signal. Alternatively, from the firstand second signals a primary reference which is a significant functionof the physiological measurement components of the first and secondsignals may be derived. This approach may also comprise the step ofinputting the primary reference into a correlation canceler to producean output signal which is a significant function of the first or secondsignal's motion artifact component.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an ideal plethysmographic waveform.

FIG. 2 schematically illustrates the cross-sectional structure of atypical finger.

FIG. 3 illustrates a plethysmographic waveform which includes amotion-induced erratic signal portion.

FIG. 4 a illustrates a schematic diagram of a physiological monitor, tocompute primary physiological signals, incorporating a processor of thepresent invention, and a correlation canceler.

FIG. 4 b illustrates a schematic diagram of a physiological monitor, tocompute secondary erratic signals, incorporating a processor of thepresent invention, and a correlation canceler.

FIG. 5 a illustrates an example of an adaptive noise canceler whichcould be employed in a physiological monitor, to compute primaryphysiological signals, which also incorporates the processor of thepresent invention.

FIG. 5 b illustrates an example of an adaptive noise canceler whichcould be employed in a physiological monitor, to compute secondarymotion artifact signals, which also incorporates the processor of thepresent invention.

FIG. 5 c illustrates the transfer function of a multiple notch filter.

FIG. 6 a illustrates a schematic absorbing material comprising Nconstituents within an absorbing material.

FIG. 6 b illustrates another schematic absorbing material comprising Nconstituents, including one mixed layer, within an absorbing material.

FIG. 6 c illustrates another schematic absorbing material comprising Nconstituents, including two mixed layers, within an absorbing material.

FIG. 7 a illustrates a schematic diagram of a monitor, to computeprimary and secondary signals, incorporating a processor of the presentinvention, a plurality of signal coefficients ω₁, ω₂, . . . ω_(n), and acorrelation canceler.

FIG. 7 b illustrates the ideal correlation canceler energy or poweroutput as a function of the signal coefficients ω₁, ω₂, . . . ω_(n). Inthis particular example, ω₃=ω_(a) and ω₇=ω_(v).

FIG. 7 c illustrates the non-ideal correlation canceler energy or poweroutput as a function of the signal coefficients ω₁, ω₂, . . . ω_(n). Inthis particular example, ω₃=ω_(a) and ω₇=ω_(v).

FIG. 8 is a schematic model of a joint process estimator comprising aleast-squares lattice predictor and a regression filter.

FIG. 9 is a flowchart representing a subroutine capable of implementinga joint process estimator as modeled in FIG. 8.

FIG. 10 is a schematic model of a joint process estimator with aleast-squares lattice predictor and two regression filters.

FIG. 11 is an example of a physiological monitor incorporating aprocessor of the present invention and a correlation canceler within amicroprocessor. This physiological monitor is specifically designed tomeasure a plethysmographic waveform or a motion artifact waveform andperform oximetry measurements.

FIG. 12 is a graph of oxygenated and deoxygenated hemoglobin absorptioncoefficients vs. wavelength.

FIG. 13 is a graph of the ratio of the absorption coefficients ofdeoxygenated hemoglobin divided by oxygenated hemoglobin vs. wavelength.

FIG. 14 is an expanded view of a portion of FIG. 12 marked by a circlelabeled 13.

FIG. 15 illustrates a signal measured at a first red wavelengthλa=λred1=650 nm for use in a processor of the present inventionemploying the ratiometric method for determining either the primaryreference n′(t) or the secondary reference s′(t) and for use in acorrelation canceler, such as an adaptive noise canceler. The measuredsignal comprises a primary portion s_(λa)(t) and a secondary portionn_(λa)(t).

FIG. 16 illustrates a signal measured at a second red wavelengthλb=λred2=685 nm for use in a processor of the present inventionemploying the ratiometric method for determining the secondary referencen′(t) or the primary reference s′(t). The measured signal comprises aprimary portion s_(λb)(t) and a secondary portion n_(λb)(t).

FIG. 17 illustrates a signal measured at an infrared wavelengthλc=λIR=940 nm for use in a correlation canceler. The measured signalcomprises a primary portion s_(λc)(t) and a secondary portion n_(λc)(t).

FIG. 18 illustrates the secondary reference n′(t) determined by aprocessor of the present invention using the ratiometric method.

FIG. 19 illustrates the primary reference s′(t) determined by aprocessor of the present invention using the ratiometric method.

FIG. 20 illustrates a good approximation s″_(λa)(t) to the primaryportion s_(λa)(t) of the signal s_(λa)(t) measured at λa=λred1=650 nmestimated by correlation cancellation with a secondary reference n′(t)determined by the ratiometric method.

FIG. 21 illustrates a good approximation s″_(λc)(t) to the primaryportion s_(λc)(t) of the signal s_(λc)(t) measured at λc=λIR=940 nmestimated by correlation cancellation with a secondary reference n′(t)determined by the ratiometric method.

FIG. 22 illustrates a good approximation n″_(λa)(t) to the secondaryportion n_(λa)(t) of the signal S_(λa)(t) measured at λa=λred1=650 nmestimated by correlation cancellation with a primary reference s′(t)determined by the ratiometric method.

FIG. 23 illustrates a good approximation n″_(λc)(t) to the secondaryportion n_(λc)(t) of the signal S_(λc)(t) measured at λc=λIR=940 nmestimated by correlation cancelation with a primary reference s′(t)determined by the ratiometric method.

FIG. 24 illustrates a signal measured at a red wavelength λa=λred=660 nmfor use in a processor of the present invention employing the constantsaturation method for determining the secondary reference n′(t) or theprimary reference s′(t) and for use in a correlation canceler. Themeasured signal comprises a primary portion s_(λa)(t) and a secondaryportion n_(λa)(t).

FIG. 25 illustrates a signal measured at an infrared wavelengthλb=λIR=940 nm for use in a processor of the present invention employingthe constant saturation method for determining the secondary referencen′(t) or the primary reference s′(t) and for use in a correlationcanceler. The measured signal comprises a primary portion s_(λb)(t) anda secondary portion n_(λb)(t).

FIG. 26 illustrates the secondary reference n′(t) determined by aprocessor of the present invention using the constant saturation method.

FIG. 27 illustrates the primary reference s′(t) determined by aprocessor of the present invention using the constant saturation method.

FIG. 28 illustrates a good approximation s″_(λa)(t) to the primaryportion s_(λa)(t) of the signal S_(λa)(t) measured at λa=λred=660 nmestimated by correlation cancelation with a secondary reference n′(t)determined by the constant saturation method.

FIG. 29 illustrates a good approximation s″_(λb)(t) to the primaryportion s_(λb)(t) of the signal S_(λb)(t) measured at λb=λIR=940 nmestimated by correlation cancelation with a secondary reference n′(t)determined by the constant saturation method.

FIG. 30 illustrates a good approximation n″_(λa)(t) to the secondaryportion n_(λa)(t) of the signal S_(λa)(t) measured at λa=λred=660 nmestimated by correlation cancelation with a primary reference s′(t)determined by the constant saturation method.

FIG. 31 illustrates a good approximation n″_(λb)(t) to the secondaryportion n_(λb)(t) of the signal S_(λb)(t) measured at λb=λIR=940 nmestimated by correlation cancelation with a primary reference s′(t)determined by the constant saturation method.

FIG. 32 depicts a set of 3 concentric electrodes, i.e. a tripolarelectrode sensor, to derive electrocardiography (ECG) signals, denotedas S₁, S₂ and S₃, for use with the present invention. Each of the ECGsignals contains a primary portion and a secondary portion.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

The present invention is a processor which determines either a secondaryreference n′(t) or a primary reference s′(t) for use in a correlationcanceler, such as an adaptive noise canceler. A correlation canceler mayestimate a good approximation s″(t) to a primary signal s(t) from acomposite signal S(t)=s(t)+n(t) which, in addition to the primaryportion s(t) comprises a secondary portion n(t). It may also be used toprovide a good approximation n″(t) to the secondary signal n(t). Thesecondary portion n(t) may contain one or more of a constant portion, apredictable portion, an erratic portion, a random portion, etc. Theapproximation to the primary signal s″(t) or secondary signal n″(t) isderived by removing as many of the secondary portions n(t) or primaryportions s(t) from the composite signal S(t) as possible. The constantportion and predictable portion are easily removed with traditionalfiltering techniques, such as simple subtraction, low pass, band pass,and high pass filtering. The erratic portion is more difficult to removedue to its unpredictable nature. If something is known about the erraticsignal, even statistically, it could be removed, at least partially,from the measured signal via traditional filtering techniques. However,it is often the case that no information is known about the erraticportion of the noise. In this case, traditional filtering techniques areusually insufficient. Often no information about the erratic portion ofthe measured signal is known. Thus, a correlation canceler, such as anadaptive noise canceler may be utilized in the present invention toremove or derive the erratic portion.

Generally, a correlation canceler has two signal inputs and one output.One of the inputs is either the secondary reference n′(t) or the primaryreference s′(t) which are correlated, respectively, to the secondarysignal portions n(t) and the primary signal portions s(t) present in thecomposite signal S(t). The other input is for the composite signal S(t).Ideally, the output of the correlation canceler s″(t) or n″(t)corresponds, respectively, to the primary signal s(t) or the secondarysignal n(t) portions only. Often, the most difficult task in theapplication of correlation cancelers is determining the referencesignals n′(t) and s′(t) which are correlated to the secondary n(t) andprimary s(t) portions, respectively, of the measured signal S(t) since,as discussed above, these portions are quite difficult to isolate fromthe measured signal S(t). In the signal processor of the presentinvention, either a secondary reference n′(t) or a primary references′(t) is determined from two composite signals measured simultaneously,or nearly simultaneously, at two different wavelengths, λa and λb.

A block diagram of a generic monitor incorporating a signal processor,or reference processor, according to the present invention, and acorrelation canceler is shown in FIGS. 4 a and 4 b. Two measuredsignals, S_(λa)(t) and S_(λb)(t), are acquired by a detector 20. Oneskilled in the art will realize that for some physiologicalmeasurements, more than one detector may be advantageous. Each signal isconditioned by a signal conditioner 22 a and 22 b. Conditioningincludes, but is not limited to, such procedures as filtering thesignals to remove constant portions and amplifying the signals for easeof manipulation. The signals are then converted to digital data by ananalog-to-digital converter 24 a and 24 b. The first measured signalS_(λa)(t) comprises a first primary signal portion, labeled hereins_(λa)(t), and a first secondary signal portion, labeled hereinn_(λa)(t). The second measured signal S_(λb)(t) is at least partiallycorrelated to the first measured signal S_(λa)(t) and comprises a secondprimary signal portion, labeled herein s_(λb)(t), and a second secondarysignal portion, labeled herein n_(λb)(t). Typically the first and secondsecondary signal portions, n_(λa)(t) and n_(λb)(t), are uncorrelatedand/or erratic with respect to the primary signal portions s_(λa)(t) ands_(λb)(t). The secondary signal portions n_(λa)(t) and n_(λb)(t) areoften caused by motion of a patient. The signals S_(λa)(t) and S_(λb)(t)are input to a reference processor 26. The reference processormultiplies the second measured signal S_(λb)(t) by either a factorω_(a)=s_(λa)(t)/s_(λb)(t) or a factor ω_(v)=n_(λa)(t)/n_(λb)(t) and thensubtracts the second measured signal S_(λb)(t) from the first measuredsignal S_(λa)(t). The signal coefficient factors ω_(a) and ω_(v) aredetermined to cause either the primary signal portions s_(λa)(t) ands_(λb)(t) or the secondary signal portions n_(λa)(t) and n_(λb)(t) tocancel when the two signals S_(λa)(t) and S_(λb)(t) are subtracted.Thus, the output of the reference processor 26 is either a secondaryreference signal n′(t)=n_(λa)(t)−ω_(a) n_(λb)(t), in FIG. 4 a, which iscorrelated to both of the secondary signal portions n_(λa)(t) andn_(λb)(t) or a primary reference signal s′(t)=s_(λa)(t)−ω_(v) s_(λb)(t),in FIG. 4 b, which is correlated to both of the primary signal portionss_(λa)(t) and s_(λb)(t). A reference signal n′(t) or s′(t) is input,along with one of the measured signals S_(λa)(t) or S_(λb)(t), to acorrelation canceler 27 which uses the reference signal n′(t) or s′(t)to remove either the secondary signal portions n_(λa)(t) or n_(λb)(t) orthe primary signal portions s_(λa)(t) or s_(λb)(t) from the measuredsignal S_(λa)(t) or S_(λb)(t). The output of the correlation canceler 27is a good approximation s″(t) or n″(t) to either the primary s(t) or thesecondary n(t) signal components. The approximation s″(t) or n″(t) isdisplayed on the display 28.

An adaptive noise canceler 30, an example of which is shown in blockdiagram form in FIG. 5 a, is employed to remove either one of theerratic, secondary signal portions n_(λa)(t) and n_(λb)(t) from thefirst and second signals S_(λa)(t) and S_(λb)(t). The adaptive noisecanceler 30, which performs the functions of a correlation canceler, inFIG. 5 a has as one input a sample of the secondary reference n′(t)which is correlated to the secondary signal portions n_(λa)(t) andn_(λb)(t). The secondary reference n′(t) is determined from the twomeasured signals S_(λa)(t) and S_(λb)(t) by the processor 26 of thepresent invention as described herein. A second input to the adaptivenoise canceler, is a sample of either the first or second compositemeasured signals S_(λa)(t)=s_(λa)(t)+n_(λa)(t) orS_(λb)(t)=s_(λb)(t)+n_(λb)(t).

The adaptive noise canceler 30, in FIG. 5 b, may also be employed toremove either one of primary signal portions s_(λa)(t) and s_(λb)(t)from the first and second signals S_(λa)(t) and S_(λb)(t). The adaptivenoise canceler 30 has as one input a sample of the primary references′(t) which is correlated to the primary signal portions s_(λa)(t) ands_(λb)(t). The primary reference s′(t) is determined from the twomeasured signals S_(λa)(t) and S_(λb)(t) by the processor 26 of thepresent invention as described herein. A second input to the adaptivenoise canceler 30 is a sample of either the first or second measuredsignals S_(λa)(t)=s_(λa)(t)+n_(λa)(t) or S_(λb)(t)=s_(λb)(t)+n_(λb)(t).

The adaptive noise canceler 30 functions to remove frequencies common toboth the reference n′(t) or s′(t) and the measured signal S_(λa)(t) orS_(λb)(t). Since the reference signals are correlated to either thesecondary signal portions n_(λa)(t) and n_(λb)(t) or the primary signalportions s_(λa)(t) and s_(λb)(t), the reference signals will becorrespondingly erratic or well behaved. The adaptive noise canceler 30acts in a manner which may be analogized to a dynamic multiple notchfilter based on the spectral distribution of the reference signal n′(t)or s′(t).

Referring to FIG. 5 c, the transfer function of a multiple notch filteris shown. The notches, or dips in the amplitude of the transferfunction, indicate frequencies which are attenuated or removed when acomposite measured signal passes through the notch filter. The output ofthe notch filter is the composite signal having frequencies at which anotch was present removed. In the analogy to an adaptive noise canceler30, the frequencies at which notches are present change continuouslybased upon the inputs to the adaptive noise canceler 30.

The adaptive noise canceler 30 shown in FIGS. 5 a and 5 b produces anoutput signal, labeled herein as s″_(λa)(t), s_(λb)(t), n″_(λa)(t) orn″_(λb)(t) which is fed back to an internal processor 32 within theadaptive noise canceler 30. The internal processor 32 automaticallyadjusts its own transfer function according to a predetermined algorithmsuch that the output of the internal processor 32, labeled b(t) in FIG.5 a or c(t) in FIG. 5 b, closely resembles either the secondary signalportion n_(λa)(t) or n_(λb)(t) or the primary signal portion s_(λa)(t)or s_(λb)(t). The output b(t) of the internal processor 32 in FIG. 5 ais subtracted from the measured signal, S_(λa)(t) or S_(λb)(t), yieldinga signal output s″_(λa)(t)=s_(λa)(t)+n_(λa)(t)−b_(λa)(t) or a signaloutput s″_(λb)(t)=s_(λb)(t)+n_(λb)(t)−b_(λb)(t). The internal processoroptimizes s″_(λa)(t) or s″_(λb)(t) such that s″_(λa)(t) or s″_(λb)(t) isapproximately equal to the primary signal s_(λa)(t) or s_(λb)(t),respectively. The output c(t) of the internal processor 32 in FIG. 5 bis subtracted from the measured signal, S_(λa)(t) or S_(λb)(t), yieldinga signal output given by n″_(λa)(t)=s_(λa)(t)+n_(λa)(t)−c_(λa)(t) or asignal output given by n″_(λb)(t)=s_(λb)(t)+n_(λb)(t)−c_(λb)(t). Theinternal processor optimizes n″_(λa)(t) or n″_(λb)(t) such thatn″_(λa)(t) or n″_(λb)(t) is approximately equal to the secondary signaln_(λa)(t) or n_(λb)(t), respectively.

One algorithm which may be used for the adjustment of the transferfunction of the internal processor 32 is a least-squares algorithm, asdescribed in Chapter 6 and Chapter 12 of the book Adaptive SignalProcessing by Bernard Widrow and Samuel Stearns, published by PrenticeHall, copyright 1985. This entire book, including Chapters 6 and 12, ishereby incorporated herein by reference.

Adaptive processors 30 in FIGS. 5 a and 5 b have been successfullyapplied to a number of problems including antenna sidelobe canceling,pattern recognition, the elimination of periodic interference ingeneral, and the elimination of echoes on long distance telephonetransmission lines. However, considerable ingenuity is often required tofind a suitable reference signal n′(t) or s′(t) since the portionsn_(λa)(t), n_(λb)(t), s_(λa)(t) and s_(λb)(t) cannot easily be separatedfrom the measured signals S_(λa)(t) and S_(λb)(t). If either the actualsecondary portion n_(λa)(t) or n_(λb)(t) or the primary signal portions_(λa)(t) or s_(λb)(t) were a priori available, techniques such ascorrelation cancellation would not be necessary. The determination of asuitable reference signal n′(t) or s′(t) from measurements taken by amonitor incorporating a reference processor of the present invention isone aspect of the present invention.

Generalized Determination of Primary and Secondary Reference Signals

An explanation which describes how the reference signals n′(t) and s′(t)may be determined follows. A first signal is measured at, for example, awavelength λa, by a detector yielding a signal S_(λa)(t):

S _(λa)(t)=s _(λa)(t)+n _(λa)(t)  (I)

where s_(λa)(t) is the primary signal and n_(λa)(t) is the secondarysignal.

A similar measurement is taken simultaneously, or nearly simultaneously,at a different wavelength, λb, yielding:

S _(λb)(t)=s _(λb)(t)+n _(λb)(t)  (2)

Note that as long as the measurements, S_(λa)(t) and S_(λb)(t), aretaken substantially simultaneously, the secondary signal components,n_(λa)(t) and n_(λb)(t), will be correlated because any random orerratic functions will affect each measurement in nearly the samefashion. The well behaved primary signal components, s_(λa)(t) ands_(λb)(t), will also be correlated to one another.

To obtain the reference signals n′(t) and s′(t), the measured signalsS_(λa)(t) and S_(λb)(t) are transformed to eliminate, respectively, theprimary or secondary signal components. One way of doing this is to findproportionality constants, ω_(a) and ω_(v), between the primary signalss_(λa)(t) and s_(λb)(t) and secondary signals n_(λa)(t) and n_(λb)(t)such that:

s _(λa)(t)=ω_(a) s _(λb)(t)

n _(λa)(t)=ω_(v) n _(λb)(t).  (3)

These proportionality relationships can be satisfied in manymeasurements, including but not limited to absorption measurements andphysiological measurements. Additionally, in most measurements, theproportionality constants ω_(a) and ω_(v) can be determined such that:

n _(λa)(t)≠ω_(a) n _(λb)(t)

s _(λa)(t)≠ω_(v) s _(λb)(t).  (4)

Multiplying equation (2) by ω_(a) and then subtracting equation (2) fromequation (1) results in a single equation wherein the primary signalterms s_(λa)(t) and s_(λb)(t) cancel, leaving:

n′(t)=S _(λa)(t)−ω_(a) S _(λb)(t)=n _(λa)(t)−ω_(a) n _(λb)(t);  (5a)

a non-zero signal which is correlated to each secondary signal portionn_(λa)(t) and n_(λb)(t) and can be used as the secondary reference n′(t)in a correlation canceler such as an adaptive noise canceler.

Multiplying equation (2) by ω_(v) and then subtracting equation (2) fromequation (1) results in a single equation wherein the secondary signalterms n_(λa)(t) and n_(λb)(t) cancel, leaving:

s′(t)=S _(λa)(t)−ω_(v) S _(λb)(t)=s _(λa)(t)−ω_(v) s _(λb)(t);  (5b)

a non-zero signal which is correlated to each of the primary signalportions s_(λa)(t) and s_(λb)(t) and can be used as the signal references′(t) in a correlation canceler such as an adaptive noise canceler.

Example of Determination of Primary and Secondary Reference Signals inan Absorptive System

Correlation canceling is particularly useful in a large number ofmeasurements generally described as absorption measurements. An exampleof an absorption type monitor which can advantageously employcorrelation canceling, such as adaptive noise canceling, based upon areference n′(t) or s′(t) determined by a processor of the presentinvention is one which determines the concentration of an energyabsorbing constituent within an absorbing material when the material issubject to change. Such changes can be caused by forces about whichinformation is desired or primary, or alternatively, by random orerratic secondary forces such as a mechanical force on the material.Random or erratic interference, such as motion, generates secondarycomponents in the measured signal. These secondary components can beremoved or derived by the correlation canceler if a suitable secondaryreference n′(t) or primary reference s′(t) is known.

A schematic N constituent absorbing material comprising a container 42having N different absorbing constituents, labeled A₁, A₂, A₃, . . .A_(N), is shown schematically in FIG. 6 a. The constituents A₁ throughA_(N) in FIG. 6 a are arranged in a generally orderly, layered fashionwithin the container 42. An example of a particular type of absorptivesystem is one in which light energy passes through the container 42 andis absorbed according to the generalized Beer-Lambert Law of lightabsorption. For light of wavelength λa, this attenuation may beapproximated by:

$\begin{matrix}{I = {I_{o}{\exp\left( {{- \sum\limits_{i = 1}^{N}} \in_{i,{\lambda \; a}}{c_{i}x_{i}}} \right)}}} & (6)\end{matrix}$

Initially transforming the signal by taking the natural logarithm ofboth sides and manipulating terms, the signal is transformed such thatthe signal components are combined by addition rather thanmultiplication, i.e.:

$\begin{matrix}{S_{\lambda \; a} = {{\ln \left( {I_{o}\text{/}I} \right)} = {\sum\limits_{i = 1}^{N}{\in_{i,{\lambda \; a}}{c_{i}x_{i}}}}}} & (7)\end{matrix}$

where I₀ is the incident light energy intensity; I is the transmittedlight energy intensity; ε_(i,λa) is the absorption coefficient of thei^(th) constituent at the wavelength λa; x_(i)(t) is the optical pathlength of i^(th) layer, i.e., the thickness of material of the i^(th)layer through which optical energy passes; and c_(i)(t) is theconcentration of the i^(th) constituent in the volume associated withthe thickness x_(i)(t). The absorption coefficients ε₁ through ε_(N) areknown values which are constant at each wavelength. Most concentrationsc₁(t) through c_(N)(t) are typically unknown, as are most of the opticalpath lengths x_(i)(t) of each layer. The total optical path length isthe sum of each of the individual optical path lengths x_(i)(t) of eachlayer.

When the material is not subject to any forces which cause change in thethicknesses of the layers, the optical path length of each layer,x_(i)(t), is generally constant. This results in generally constantattenuation of the optical energy and thus, a generally constant offsetin the measured signal. Typically, this portion of the signal is oflittle interest since knowledge about a force which perturbs thematerial is usually desired. Any signal portion outside of a knownbandwidth of interest, including the constant undesired signal portionresulting from the generally constant absorption of the constituentswhen not subject to change, should be removed. This is easilyaccomplished by traditional band pass filtering techniques. However,when the material is subject to forces, each layer of constituents maybe affected by the perturbation differently than each other layer. Someperturbations of the optical path lengths of each layer x_(i)(t) mayresult in excursions in the measured signal which represent desired orprimary information. Other perturbations of the optical path length ofeach layer x_(i)(t) cause undesired or secondary excursions which maskprimary information in the measured signal. Secondary signal componentsassociated with secondary excursions must also be removed to obtainprimary information from the measured signal. Similarly, the ability tocompute secondary signal components caused by secondary excursionsdirectly allows one to obtain primary signal components from themeasured signal via simple subtraction, or correlation cancellationtechniques.

The correlation canceler may selectively remove from the compositesignal, measured after being transmitted through or reflected from theabsorbing material, either the secondary or the primary signalcomponents caused by forces which perturb or change the materialdifferently from the forces which perturbed or changed the material tocause respectively, either the primary or secondary signal component.For the purposes of illustration, it will be assumed that the portion ofthe measured signal which is deemed to be the primary signal s_(λa)(t)is the attenuation term ε₅c₅x₅(t) associated with a constituent ofinterest, namely A₅, and that the layer of constituent A₅ is affected byperturbations different than each of the layers of other constituents A₁through A₄ and A₆ through A_(N). An example of such a situation is whenlayer A₅ is subject to forces about which information is deemed to beprimary and, additionally, the entire material is subject to forceswhich affect each of the layers. In this case, since the total forceaffecting the layer of constituent A₅ is different than the total forcesaffecting each of the other layers and information is deemed to beprimary about the forces and resultant perturbation of the layer ofconstituent A₅, attenuation terms due to constituents A₁ through A₄ andA₆ through A_(N) make up the secondary signal portion n_(λa)(t). Even ifthe additional forces which affect the entire material cause the sameperturbation in each layer, including the layer of A₅, the total forceson the layer of constituent A₅ cause it to have different totalperturbation than each of the other layers of constituents A₁ through A₄and A₆ through A_(N).

It is often the case that the total perturbation affecting the layersassociated with the secondary signal components is caused by random orerratic forces. This causes the thickness of layers to changeerratically and the optical path length of each layer, x_(i)(t), tochange erratically, thereby producing a random or erratic secondarysignal component n_(λa)(t). However, regardless of whether or not thesecondary signal portion n_(λa)(t) is erratic, the secondary signalcomponent n_(λa)(t) can be either removed or derived via a correlationcanceler, such as an adaptive noise canceler, having as one input,respectively, a secondary reference n′(t) or a primary reference s′(t)determined by a processor of the present invention as long as theperturbation on layers other than the layer of constituent A₅ isdifferent than the perturbation on the layer of constituent A₅. Thecorrelation canceler yields a good approximation to either the primarysignal s_(λa)(t) or the secondary signal n_(λa)(t). In the event that anapproximation to the primary signal is obtained, the concentration ofthe constituent of interest, c₅(t), can often be determined since insome physiological measurements, the thickness of the primary signalcomponent, x₅(t) in this example, is known or can be determined.

The correlation canceler utilized a sample of either the secondaryreference n′(t) or the primary reference s′(t) determined from twosubstantially simultaneously measured signals S_(λa)(t) and S_(λb)(t).S_(λa)(t) is determined as above in equation (7). S_(λb)(t) isdetermined similarly at a different wavelength λb. To find either thesecondary reference n′(t) or the primary reference s′(t), attenuatedtransmitted energy is measured at the two different wavelengths λa andλb and transformed via logarithmic conversion. The signals S_(λa)(t) andS_(λb)(t) can then be written (logarithm converted) as:

$\begin{matrix}{{S_{\lambda \; a}(t)} = {\in_{5,{\lambda \; a}}{{c_{5}{x_{5}(t)}} + \sum\limits_{i = 1}^{4}} \in_{i,{\lambda \; a}}{{c_{i}x_{i}} + \sum\limits_{i = 6}^{N}} \in_{i,{\lambda \; a}}{c_{i}x_{i}}}} & (8) \\{S_{\lambda \; {a{(t)}}} = {{ɛ_{5,{\lambda \; a}}c_{5}{x_{5}(t)}} + {n_{\lambda \; a}(t)}}} & (9) \\{S_{\lambda \; {b{(t)}}} = {\in_{5,{\lambda \; b}}{{c_{5}{x_{5}(t)}} + \sum\limits_{i = 1}^{4}} \in_{i,{\lambda \; b}}{{c_{i}x_{i}} + \sum\limits_{i = 6}^{N}} \in_{i,{\lambda \; b}}{c_{i}x_{i}}}} & (10) \\{S_{\lambda \; {b{(t)}}} = {{ɛ_{5,{\lambda \; b}}c_{5}{x_{5}(t)}} + {n_{\lambda \; b}(t)}}} & (11)\end{matrix}$

Further transformations of the signals are the proportionalityrelationships defining ω_(a) and ω_(v), similarly to equation (3), whichallows determination of a noise reference n′(t) and a primary references′(t). These are:

ε_(5,λa)=ω_(a)ε_(5,λb)  (12a)

n_(λa)=ω_(v)n_(λb)  (12b)

where

n_(λa)≠ω_(a)n_(λb)  (13a)

ε_(5,λa)≠ω_(v)ε_(5,λb)  (13b)

It is often the case that both equations (12) and (13) can besimultaneously satisfied. Multiplying equation (11) by ω_(a) andsubtracting the result from equation (9) yields a non-zero secondaryreference which is a linear sum of secondary signal components:

$\begin{matrix}{\mspace{79mu} {{n^{\prime}(t)} = {{{S_{\lambda \; a}(t)} - {\omega_{a}{S_{\lambda \; b}(t)}}} = {{n_{\lambda \; a}(t)} - {\omega_{a}{n_{\lambda \; b}(t)}}}}}} & \left( {14a} \right) \\{= {\sum\limits_{i = 1}^{4}{\in_{i,{\lambda \; a}}{{c_{i}{x_{i}(t)}} + \sum\limits_{i = 6}^{N}} \in_{i,{\lambda \; a}}{{c_{i}{x_{i}(t)}} - {\sum\limits_{i = 1}^{4}\omega_{a}}} \in_{i,{\lambda \; b}}{{c_{i}{x_{i}(t)}} + {\sum\limits_{i = 6}^{N}\omega_{a}}} \in_{i,{\lambda \; b}}{c_{i}{x_{i}(t)}}}}} & \left( {15a} \right) \\{\mspace{79mu} {= {{\sum\limits_{i = 1}^{4}{c_{i}{{x_{i}(t)}\left\lbrack {\in_{i,{\lambda \; a}}{- \omega_{a}} \in_{i,{\lambda \; b}}} \right\rbrack}}} + {\sum\limits_{i = 6}^{N}{c_{i}{{x_{i}(t)}\left\lbrack {\in_{i,{\lambda \; a}}{- \omega_{a}} \in_{i,{\lambda \; b}}} \right\rbrack}}}}}} & \left( {16a} \right)\end{matrix}$

Multiplying equation (11) by ω_(v) and subtracting the result fromequation (9) yields a primary reference which is a linear sum of primarysignal components:

$\begin{matrix}{{s^{\prime}(t)} = {{{S_{\lambda \; a}(t)} - {\omega_{v}{S_{\lambda \; b}(t)}}} = {{s_{\lambda \; a}(t)} - {\omega_{v}{s_{\lambda \; b}(t)}}}}} & \left( {14b} \right) \\{\mspace{45mu} {= {{c_{5}{x_{5}(t)}ɛ_{5,{\lambda \; a}}} - {\omega_{v}c_{5}{x_{5}(t)}ɛ_{5,{\lambda \; b}}}}}} & \left( {15b} \right) \\{\mspace{45mu} {= {c_{5}{{{x_{5}(t)}\left\lbrack {ɛ_{5,{\lambda \; a}} - {\omega_{v}ɛ_{5,{\lambda \; b}}}} \right\rbrack}.}}}} & \left( {16b} \right)\end{matrix}$

A sample of either the secondary reference n′(t) or the primaryreference s′(t), and a sample of either measured signal S_(λa)(t) orS_(λb)(t), are input to a correlation canceler 27, such as an adaptivenoise canceler 30, an example of which is shown in FIGS. 5 a and 5 b anda preferred example of which is discussed herein under the headingPREFERRED CORRELATION CANCELER USING A JOINT PROCESS ESTIMATORIMPLEMENTATION. The correlation canceler 27 removes either the secondaryportion n_(λa)(t) or n_(λb)(t), or the primary portions, s_(λa)(t) ors_(λb)(t), of the measured signal yielding a good approximation toeither the primary signals s″_(λa)(t)≈ε_(5,λa)c₅x₅(t) ors″_(λb)(t)≈ε_(5,λb)c₅x₅(t) or the secondary signals n″_(λa)(t)≈n_(λa)(t)or n″_(λb)(t)≈n_(λb)(t). In the event that the primary signals areobtained, the concentration c₅(t) may then be determined from theapproximation to the primary signal s″_(λa)(t) or s″_(λb)(t) accordingto:

c ₅(t)≈s″ _(λa)(t)/ε_(5,λa) x ₅(t)c ₅(t)≈s″ _(λb)(t)/ε_(5,λb) x₅(t)  (17)

As discussed previously, the absorption coefficients are constant ateach wavelength λa and λb and the thickness of the primary signalcomponent, x₅(t) in this example, is often known or can be determined asa function of time, thereby allowing calculation of the concentrationc₅(t) of constituent A₅.

Determination of Concentration or Saturation in a Volume Containing Morethan One Constituent

Referring to FIG. 6 b, another material having N different constituentsarranged in layers is shown. In this material, two constituents A₅ andA₆ are found within one layer having thickness x₅,6(t)=x₅(t)+x₆(t),located generally randomly within the layer. This is analogous tocombining the layers of constituents A₅ and A₆ in FIG. 6 a. Acombination of layers, such as the combination of layers of constituentsA₅ and A₆, is feasible when the two layers are under the same totalforces which result in the same change of the, optical path lengthsx₅(t) and x₆(t) of the layers.

Often it is desirable to find the concentration or the saturation, i.e.,a percent concentration, of one constituent within a given thicknesswhich contains more than one constituent and is subject to uniqueforces. A determination of the concentration or the saturation of aconstituent within a given volume may be made with any number ofconstituents in the volume subject to the same total forces andtherefore under the same perturbation or change. To determine thesaturation of one constituent in a volume comprising many constituents,as many measured signals as there are constituents which absorb incidentlight energy are necessary. It will be understood that constituentswhich do not absorb light energy are not consequential in thedetermination of saturation. To determine the concentration, as manysignals as there are constituents which absorb incident light energy arenecessary as well as information about the sum of concentrations.

It is often the case that a thickness under unique motion contains onlytwo constituents. For example, it may be desirable to know theconcentration or saturation of A₅ within a given volume which containsA₅ and A₆. In this case, the primary signals s_(λa)(t) and s_(λb)(t)comprise terms related to both A₅ and A₆ so that a determination of theconcentration or saturation of A₅ or A₆ in the volume may be made. Adetermination of saturation is discussed herein. It will be understoodthat the concentration of A₅ in a volume containing both A₅ and A₆ couldalso be determined if it is known that A₅+A₆=1, i.e., that there are noconstituents in the volume which do not absorb incident light energy atthe particular measurement wavelengths chosen. Then measured signalsS_(λa)(t) and S_(λb)(t) can be written (logarithm converted) as:

$\begin{matrix}{{S_{\lambda \; a}(t)} = {{ɛ_{5,{\lambda \; a}}c_{5}{x_{5,6}(t)}} + {ɛ_{6,{\lambda \; a}}c_{6}{x_{5,6}(t)}} + {n_{\lambda \; a}(t)}}} & \left( {18a} \right) \\{\mspace{59mu} {{= {{s_{\lambda \; a}(t)} + {n_{\lambda \; a}(t)}}};}} & \left( {18b} \right) \\{{S_{\lambda \; b}(t)} = {{ɛ_{5,{\lambda \; b}}c_{5}{x_{5,6}(t)}} + {ɛ_{6,{\lambda \; b}}c_{6}{x_{5,6}(t)}} + {m_{\lambda \; b}(t)}}} & \left( {19a} \right) \\{\mspace{59mu} {= {{s_{\lambda \; b}(t)} + {{n_{\lambda \; b}(t)}.}}}} & \left( {19b} \right)\end{matrix}$

It is also often the case that there may be two or more thicknesseswithin a medium each containing the same two constituents but eachexperiencing a separate motion as in FIG. 6 c. For example, it may bedesirable to know the concentration or saturation of A₅ within a givenvolume which contains A₅ and A₆ as well as the concentration orsaturation of A₃ within a given volume which contains A₃ and A₄, A₃ andA₄ having the same constituency as A₅ and A₆, respectively. In thiscase, the primary signals s_(λa)(t) and s_(λb)(t) again comprise termsrelated to both A₅ and A₆ and portions of the secondary signalsn_(λa)(t) and n_(λb)(t) comprise terms related to both A₃ and A₄. Thelayers, A₃ and A₄, do not enter into the primary equation because theyare assumed to be perturbed by random or erratic secondary forces whichare uncorrelated with the primary force. Since constituents 3 and 5 aswell as constituents 4 and 6 are taken to be the same, they have thesame absorption coefficients. i.e. ε_(3,λa)=ε_(5,λa), ε_(3,λb)=ε_(5,λb),ε_(4,λa)=ε_(6,λa) and ε_(4,λb)=ε_(6,λb). Generally speaking, however, A₃and A₄ will have different concentrations than A₅ and A₆ and willtherefore have a different saturation. Consequently a single constituentwithin a medium may have one or more saturations associated with it. Theprimary and secondary signals according to this model may be written as:

$\begin{matrix}{{{s_{\lambda \; a}(t)} = {\left\lbrack {{ɛ_{5,{\lambda \; a}}c_{5}} + {ɛ_{6,{\lambda \; a}}c_{6}}} \right\rbrack {x_{5,6}(t)}}}{{n_{\lambda \; a}(t)} = {\left\lbrack {{ɛ_{5,{\lambda \; a}}c_{3}} + {ɛ_{6,{\lambda \; a}}c_{4}}} \right\rbrack {x_{3,4}(t)}}}} & \left( {20a} \right) \\{{+ \sum\limits_{i = 1}^{2}} \in_{i,{\lambda \; a}}{{c_{i}{x_{i}(t)}} + \sum\limits_{i = 7}^{n}} \in_{i,{\lambda \; a}}{c_{i}{x_{i}(t)}}} & \left( {20b} \right) \\{{n_{\lambda \; a}(t)} = {{\left\lbrack {{ɛ_{5,{\lambda \; a}}c_{3}} + {ɛ_{6,{\lambda \; a}}c_{4}}} \right\rbrack {x_{3,4}(t)}} + {n_{\lambda \; a}(t)}}} & \left( {20c} \right) \\{{{s_{\lambda \; b}(t)} = {\left\lbrack {{ɛ_{5,{\lambda \; b}}c_{5}} + {ɛ_{6,{\lambda \; b}}c_{6}}} \right\rbrack {x_{5,6}(t)}}}{{n_{\lambda \; b}(t)} = {\left\lbrack {{ɛ_{5,{\lambda \; b}}c_{3}} + {ɛ_{6,{\lambda \; b}}c_{4}}} \right\rbrack {x_{3,4}(t)}}}} & \left( {21a} \right) \\{{+ \sum\limits_{i = 1}^{2}} \in_{i,{\lambda \; b}}{{c_{i}{x_{i}(t)}} + \sum\limits_{i = 7}^{N}} \in_{i,{\lambda \; b}}{c_{i}{{x_{i}(t)}.}}} & \left( {21b} \right) \\{{n_{\lambda \; b}(t)} = {{\left\lbrack {{ɛ_{5,{\lambda \; b}}c_{3}} + {ɛ_{6,{\lambda \; b}}c_{4}}} \right\rbrack {x_{3,4}(t)}} + {n_{\lambda \; b}(t)}}} & \left( {21c} \right)\end{matrix}$

where signals n_(λa)(t) and n_(λb)(t) are similar to the secondarysignals n_(λa)(t) and n_(λb)(t) except for the omission of the 3, 4layer.

Any signal portions whether primary or secondary, outside of a knownbandwidth of interest, including the constant undesired secondary signalportion resulting from the generally constant absorption of theconstituents when not under perturbation, should be removed to determinean approximation to either the primary signal or the secondary signalwithin the bandwidth of interest. This is easily accomplished bytraditional band pass filtering techniques. As in the previous example,it is often the case that the total perturbation or change affecting thelayers associated with the secondary signal components is caused byrandom or erratic forces, causing the thickness of each layer, or theoptical path length of each layer, x_(i)(t), to change erratically,producing a random or erratic secondary signal component n_(λa)(t).Regardless of whether or not the secondary signal portion n_(λa)(t) iserratic, the secondary signal component n_(λa)(t) can be removed orderived via a correlation canceler, such as an adaptive noise canceler,having as one input a secondary reference n′(t) or a primary references′(t) determined by a processor of the present invention as long as theperturbation in layers other than the layer of constituents A₅ and A₆ isdifferent than the perturbation in the layer of constituents A₅ and A₆.Either the erratic secondary signal components n_(λa)(t) and n_(λb)(t)or the primary components s_(λa)(t) and s_(λb)(t) may advantageously beremoved from equations (18) and (19), or alternatively equations (20)and (21), by a correlation canceler. The correlation canceler, again,requires a sample of either the primary reference s′(t) or the secondaryreference n′(t) and a sample of either of the composite signalsS_(λa)(t) or S_(λb)(t) of equations (18) and (19).

Determination of Primary and Secondary Reference Signals for SaturationMeasurements

Two methods which may be used by a processor of the present invention todetermine either the secondary reference n′(t) or the primary references′(t) are a ratiometric method and a constant saturation method. Oneembodiment of a physiological monitor incorporating a processor of thepresent invention utilizes the ratiometric method wherein the twowavelengths λa and λb, at which the signals S_(λa)(t) and S_(λb)(t) aremeasured, are specifically chosen such that a relationship between theabsorption coefficients ε_(5,λa), ε_(5,λb), ε_(6,λa) and ε_(6,λb)exists, i.e.:

$\begin{matrix}{\frac{ɛ_{5,{\lambda \; b}}}{ɛ_{6,{\lambda \; b}}} = \frac{ɛ_{5,{\lambda \; a}}}{ɛ_{6,{\lambda \; a}}}} & (22)\end{matrix}$

The measured signals S_(λa)(t) and S_(λb)(t) can be factored and writtenas:

$\begin{matrix}{{S_{\lambda_{a}}(t)} = {{ɛ_{6,{\lambda \; a}}\left\lbrack {{\left( \frac{ɛ_{5,{\lambda \; a}}}{ɛ_{6,{\lambda \; a}}} \right)c_{5}{x_{5,6}(t)}} + {c_{6}{x_{5,6}(t)}}} \right\rbrack} + {n\; {\lambda_{a}(t)}}}} & \left( {23a} \right) \\{{S_{\lambda_{a}}(t)} = {{ɛ_{6,{\lambda \; a}}\begin{bmatrix}{{\left( \frac{ɛ_{5,{\lambda \; a}}}{ɛ_{6,{\lambda \; a}}} \right)c_{5}{x_{5,6}(t)}} + {c_{6}x_{5,6}(t)} +} \\{{\left( \frac{ɛ_{5,{\lambda \; a}}}{ɛ_{6,{\lambda \; a}}} \right)c_{3}{x_{3,4}(t)}} + {c_{4}{x_{3,4}(t)}}}\end{bmatrix}} + {n\; {\lambda_{a}(t)}}}} & \left( {23b} \right) \\{{S_{\lambda_{a}}(t)} = {{s_{\lambda_{a}}(t)} + {n_{\lambda_{a}}(t)}}} & \left( {23c} \right) \\{{S_{\lambda_{b}}(t)} = {{ɛ_{6,{\lambda \; b}}\left\lbrack {{\left( \frac{ɛ_{5,{\lambda \; b}}}{ɛ_{6,{\lambda \; b}}} \right)c_{5}{x_{5,6}(t)}} + {c_{6}{x_{5,6}(t)}}} \right\rbrack} + {n\; {\lambda_{b}(t)}}}} & \left( {24a} \right) \\{{S_{\lambda_{b}}(t)} = {{ɛ_{6,{\lambda \; b}}\begin{bmatrix}{{\left( \frac{ɛ_{5,{\lambda \; b}}}{ɛ_{6,{\lambda \; b}}} \right)c_{5}{x_{5,6}(t)}} + {c_{6}x_{5,6}(t)} +} \\{{\left( \frac{ɛ_{5,{\lambda \; b}}}{ɛ_{6,{\lambda \; b}}} \right)c_{3}{x_{3,4}(t)}} + {c_{4}{x_{3,4}(t)}}}\end{bmatrix}} + {n\; {\lambda_{b}(t)}}}} & \left( {24b} \right) \\{{S_{\lambda_{b}}(t)} = {{s_{\lambda_{b}}(t)} + {n_{\lambda_{b}}(t)}}} & \left( {24c} \right)\end{matrix}$

The wavelengths λa and λb, chosen to satisfy equation (22), cause theterms within the square brackets to be equal, thereby causing the termsother than n_(λa)(t) and n_(λb)(t) to be linearly dependent. Then,proportionality constants ω_(av) and ω_(e) may be found for thedetermination of a non-zero primary and secondary reference

ε_(6,λn)=ω_(av)ε_(6,λb)  (25a)

n _(λn)(t)=ω_(e) n _(λb)(t)  (25b)

ε_(6,λn)≈ω_(e)ε_(6,λb)  (25a)

n _(λn)(t)≈ω_(av) n _(λb)(t)  (26b)

It is often the case that both equations (25) and (26) can besimultaneously satisfied. Additionally, since the absorptioncoefficients of each constituent are constant with respect towavelength, the proportionality constants ω_(a)v and ω_(e) can be easilydetermined. Furthermore, absorption coefficients of other constituentsA₁ through A₂ and A₇ through A_(N) are generally unequal to theabsorption coefficients of A₃, A₄, A₅ and A₆. Thus, the secondarycomponents n_(λa) and n_(λb) are generally not made linearly dependentby the relationships of equations (22) and (25).

Multiplying equation (24) by ω_(a)v and subtracting the resultingequation from equation (23), a non-zero secondary reference isdetermined by:

n(t)=S _(λa)(t)−ω_(av) S _(λb)(t)=n _(λa)(t)−ω_(av) n _(λb)(t).  (27a)

Multiplying equation (24) by ω_(e) and subtracting the resultingequation from equation (23), a non-zero primary reference is determinedby:

s(t)=S _(λa)(t)−ω_(e) S _(λb)(t)=s _(λa)(t)−ω_(e) s _(λb)(t).  (27b)

An alternative method for determining reference signals from themeasured signals S_(λa)(t) and S_(λb)(t) using a processor of thepresent invention is the constant saturation approach. In this approach,it is assumed that the saturation of A₅ in the volume containing A₅ andA₆ and the saturation of A₃ in the volume containing A₃ and A₄ remainsrelatively constant over some period of time, i.e.:

Saturation(A ₅(t))=c ₅(t)/[c ₅(t)+c ₆(t)]  (28a)

Saturation(A ₃(t))=c ₃(t)/[c ₃(t)+c ₄(t)]  (28b)

Saturation(A ₅(t))={1+[c ₆(t)/c ₅(t)]}⁻¹  (29a)

Saturation(A ₃(t))={1+[c ₄(t)/c ₃(t)]}⁻¹  (29b)

are substantially constant over many samples of the measured signalsS_(λa) and S_(λb). This assumption is accurate over many samples sincesaturation generally changes relatively slowly in physiological systems.

The constant saturation assumption is equivalent to assuming that:

c ₅(t)/c ₆(t)=constant₁  (30a)

c ₃(t)/c ₄(t)=constant₂  (30b)

since the only other term in equations (29a) and (29b) is a constant,namely the numeral 1.

Using this assumption, the proportionality constants ω_(a) and ω_(v)which allow determination of the secondary reference signal n′(t) andthe primary reference signal s′(t) in the constant saturation methodare:

$\begin{matrix}{\omega_{v} = \frac{{ɛ_{5,{\lambda \; a}}c_{5}{x_{5,6}(t)}} + {ɛ_{6,{\lambda \; a}}c_{6}{x_{5,6}(t)}}}{\left. {{ɛ_{5,{\lambda \; b}}c_{5}{x_{5,6}(t)}} + {ɛ_{6,{\lambda \; b}}c_{6}{x_{5,6}(t)}}} \right)}} & \left( {31a} \right) \\{\mspace{31mu} {= {{s_{\lambda \; a}(t)}/{s_{\lambda \; b}(t)}}}} & \left( {32a} \right) \\{\mspace{31mu} {= \frac{{ɛ_{5,{\lambda \; a}}c_{5}} + {ɛ_{6,{\lambda \; a}}c_{6}}}{{ɛ_{5,{\lambda \; b}}c_{5}} + {ɛ_{6,{\lambda \; b}}c_{6}}}}} & \left( {33a} \right) \\{\mspace{31mu} {= \frac{{ɛ_{5,{\lambda \; a}}\left( {c_{5}/c_{6}} \right)} + ɛ_{6,{\lambda \; a}}}{{ɛ_{5,{\lambda \; b}}\left( {c_{5}/c_{6}} \right)} + ɛ_{6,{\lambda \; b}}}}} & \left( {34a} \right) \\{\mspace{31mu} {{{{\approx {{s_{\lambda \; a}^{''}(t)}/{s_{\lambda \; b}^{''}(t)}}} = {constant}_{3}};}{where}}} & \left( {35a} \right) \\{{{n_{\lambda \; a}(t)} \neq {{\omega_{a}(t)}{n_{\lambda \; b}(t)}}}{and}} & \left( {36a} \right) \\{\omega_{v} = \frac{{ɛ_{5,{\lambda \; a}}c_{3}{x_{3,4}(t)}} + {ɛ_{6,{\lambda \; a}}c_{4}{x_{3,4}(t)}}}{\left. {{ɛ_{5,{\lambda \; b}}c_{3}{x_{3,4}(t)}} + {ɛ_{6,{\lambda \; b}}c_{4}{x_{3,4}(t)}}} \right)}} & \left( {31b} \right) \\{\mspace{31mu} {= {{n_{\lambda \; a}(t)}/{n_{\lambda \; b}(t)}}}} & \left( {32b} \right) \\{\mspace{31mu} {= \frac{{ɛ_{5,{\lambda \; a}}c_{3}} + {ɛ_{6,{\lambda \; a}}c_{4}}}{{ɛ_{5,{\lambda \; b}}c_{3}} + {ɛ_{6,{\lambda \; b}}c_{4}}}}} & \left( {33b} \right) \\{\mspace{31mu} {= \frac{{ɛ_{5,{\lambda \; a}}\left( {c_{3}/c_{4}} \right)} + ɛ_{6,{\lambda \; a}}}{{ɛ_{5,{\lambda \; b}}\left( {c_{3}/c_{4}} \right)} + ɛ_{6,{\lambda \; b}}}}} & \left( {34b} \right) \\{\mspace{31mu} {{{{\approx {{n_{\lambda \; a}^{''}(t)}/{n_{\lambda \; b}^{''}(t)}}} = {constant}_{4}};}{where}}} & \left( {35b} \right) \\{{s_{\lambda \; a}(t)} \neq {{\omega_{v}(t)}{{s_{\lambda \; b}(t)}.}}} & \left( {36b} \right)\end{matrix}$

It is often the case that both equations (32) and (36) can besimultaneously satisfied to determine the proportionality constantsω_(a) and ω_(v). Additionally, the absorption coefficients at eachwavelength ε_(5,λa), ε_(6,λa), ε_(5,λb), and ε_(6,λb) are constant andthe central assumption of the constant saturation method is thatc₅(t)/c₆(t) and c₃(t)/c₄(t) are constant over many sample periods. Thus,new proportionality constants ω_(a) and ω_(v) may be determined everyfew samples from new approximations to either the primary or secondarysignal as output from the correlation canceler. Thus, the approximationsto either the primary signals s_(λa)(t) and s_(λb)(t) or the secondarysignals n_(λa)(t) and n_(λb)(t), found by the correlation canceler for asubstantially immediately preceding set of samples of the measuredsignals S_(λa)(t) and S_(λb)(t) are used in a processor of the presentinvention for calculating the proportionality constants, ω_(a) andω_(v), for the next set of samples of the measured signals S_(λa)(t) andS_(λb)(t).

Multiplying equation (19) by ω_(a) and subtracting the resultingequation from equation (18) yields a non-zero secondary referencesignal:

n′(t)=S _(λa)(t)−ω_(a) S _(λb)(t)=n _(λa)(t)−ω_(a) n _(λb)(t).  (37a)

Multiplying equation (19) by ω_(v) and subtracting the resultingequation from equation (18) yields a non-zero primary reference signal:

s′(t)=S _(λa)(t)−ω_(v) S _(λb)(t)=s _(λa)(t)−ω_(v) s _(λb)(t).  (37b)

When using the constant saturation method, it is not necessary for thepatient to remain motionless for a short period of time such that anaccurate initial saturation value can be determined by known methodsother than correlation canceling. With no erratic, motion-induced signalportions, a physiological monitor can very quickly produce an initialvalue of the saturation of A₅ in the volume containing A₅ and A₆. Anexample of a saturation calculation is given in the article“SPECTROPHOTOMETRIC DETERMINATION OF OXYGEN SATURATION OF BLOODINDEPENDENT OF THE PRESENT OF INDOCYANINE GREEN” by G. A. Mook, et al.,wherein determination of oxygen saturation in arterial blood isdiscussed. Another article discussing the calculation of oxygensaturation is “PULSE OXIMETRY: PHYSICAL PRINCIPLES, TECHNICALREALIZATION AND PRESENT LIMITATIONS” by Michael R. Neuman. Then, withvalues for the coefficients ω_(a) and ω_(v) determined, a correlationcanceler may be utilized with a secondary reference n′(t) or a primaryreference s′(t) determined by the constant saturation method.

Determination of Signal Coefficients for Primary and Secondary ReferenceSignals Using the Constant Saturation Method

The reference processor 26 of FIG. 4 a and FIG. 4 b of the presentinvention may be configured to multiply the second measured signalS_(λb)(t)=s_(λb)(t)+n_(λb)(t) by a plurality of signal coefficients ω₁,ω₂, . . . ω_(n) and then subtract each result from the first measuredsignal S_(λa)(t)=s_(λa)(t)+n_(λa)(t) to obtain a plurality of referencesignals

r′(ω,t)=s _(λa)(t)−ωs _(λb)(t)+n _(λa)(t)−ωn _(λb)(t)  (38)

for ω=ω₁, ω₂, . . . ω_(n) as shown in FIG. 7 a.

In order to determine either the primary reference s′(t) or thesecondary reference n′(t) from the above plurality of reference signalsof equation (38), signal coefficients ω_(a) and ω_(v) must be determinedfrom the plurality of signal coefficients ω₁, ω₂, . . . ω_(n). Thecoefficients ω_(a) and ω_(v) are such that they cause either the primarysignal portions s_(λa)(t) and s_(λb)(t) or the secondary signal portionsn_(λa)(t) and n_(λb)(t) to cancel or nearly cancel when they aresubstituted into the reference function r′(ω, t), e.g.

s _(λa)(t)=ω_(a) s _(λb)(t)  (39a)

n _(λa)(t)=rω _(v) n _(λb)(t)  (39b)

n′(t)=r′(ω_(a) ,t)=n _(λa)(t)−ω_(a) n _(λb)(t)  (39c)

s′(t)=r′(ω_(v) ,t)=s _(λa)(t)−ω_(v) s _(λb)(t).  (39d)

In practice, one does not usually have significant prior informationabout either the primary signal portions s_(λa)(t) and s_(λb)(t) or thesecondary signal portions n_(λa)(t) and n_(λb)(t) of the measuredsignals S_(λa)(t) and S_(λb)(t). The lack of this information makes itdifficult to determine which of the plurality of coefficients ω₁, ω₂, .. . ω_(n) correspond to the signal coefficientsω_(a)=s_(λa)(t)/s_(λb)(t) and ω_(v)=n_(λa)(t)/n_(λb)(t). Herein thepreferred approach to determine the signal coefficients ω_(a) and ω_(v)from the plurality of coefficients ω₁, ω₂, . . . ω_(n) employs the useof a correlation canceler 27, such as an adaptive noise canceler, whichtakes a first input which corresponds to one of the measured signalsS_(λa)(t) or S_(λb)(t) and takes a second input which corresponds tosuccessively each one of the plurality of reference signals r′(ω₁,t),r′(ω₂, t), . . . , r′(ω_(n), t) as shown in FIG. 7 a. For each of thereference signals r′(ω₁, t), r′(ω₂, t), . . . , r′(ω_(n), t) thecorresponding output of the correlation canceler 27 is input to anintegrator 29 for forming a cumulative output signal. The cumulativeoutput signal is subsequently input to an extremum detector 31. Thepurpose of the extremum detector 31 is to chose signal coefficientsω_(a) and ω_(v) from the set ω₁, ω₂, . . . ω_(n) by observing whichprovide a maximum in the cumulative output signal as in FIGS. 7 b and 7c. In other words, coefficients which provide a maximum integratedoutput, such as energy or power, from the correlation canceler 27correspond to the signal coefficients ω_(a) and ω_(v). One could alsoconfigure a system geometry which would require one to locate thecoefficients from the set ω₁, ω₂, . . . ω_(n) which provide a minimum orinflection in the cumulative output signal to identify the signalcoefficients ω_(a) and ω_(v).

Use of a plurality of coefficients in the processor of the presentinvention in conjunction with a correlation canceler 27 to determine thesignal coefficients ω_(a) and ω_(v) may be demonstrated by using theproperties of correlation cancellation. If x, y and z are taken to beany collection of three time varying signals, then the properties of ageneric correlation canceler C(x, y) may be defined as follows:

Property(1)C(x,y)=0 for x, y correlated

Property(2)C(x,y)=x for x, y uncorrelated

Property(3)C(x+y,z)=C(x,z)+C(y,z)  (40)

With properties (1), (2) and (3) it is easy to demonstrate that theenergy or power output of a correlation canceler with a first inputwhich corresponds to one of the measured signals S_(λa)(t) or S_(λb)(t)and a second input which corresponds to successively each one of aplurality of reference signals r′(ω₁, t), r′(ω₂, t), . . . r′(ω_(n), t)can determine the signal coefficients ω_(a) and ω_(v) needed to producethe primary reference s′(t) and secondary reference n′(t). If we take asa first input to the correlation canceler the measured signal S_(λa)(t)and as a second input the plurality of reference signals r′(ω₁, t),r′(ω₂, t), . . . , r′(ω_(n), t) then the outputs of the correlationcanceler C(S_(λa)(t), r′(ω_(j),t)) for j=1, 2, . . . , n may be writtenas

C(s _(λa(t)) +n _(λa(t)) ,s _(λa(t))−ω_(j) s _(λb(t)) +n _(λa(t)) −r_(j) n _(λb(t)))  (41)

where j=1, 2, . . . , n and we have used the expressions

r′(ω,t)=S _(λa(t)) −ωS _(λb(t))  (42)

S _(λa(t)) =s _(λa(t)) +n _(λa(t))  (43a)

S _(λb(t)) =s _(λb(t)) +n _(λb(t)).  (43b)

The use of property (3) allows one to expand equation (41) into twoterms

C(S _(λa)(t),r′(ω,t))=C(s _(λa(t)) ,s _(λa(t)) −ωs _(λb(t)) +n _(λa(t))−ωn _(λb(t)))+C(n _(λa(t)) ,s _(λa(t)) −ωs _(λb(t)) +n _(λa(t)) −ωn_(λb(t)))  (44)

so that upon use of properties (1) and (2) the correlation canceleroutput is given by

C(S _(λa(t)) ,r′(ω_(j) ,t))=s _(λa(t))δ(ω_(j−ωa))+n_(λa(t))δ(ω_(j)−ω_(v))  (45)

where δ(x) is the unit impulse function

δ(x)=0 if x≠0

δ(x)=1 if x=0.  (46)

The time variable, t, of the correlation canceler output C(S_(λa)(t),r′(ω_(j), t)) may be eliminated by computing its energy or power. Theenergy of the correlation canceler output is given by

$\begin{matrix}\begin{matrix}{{E_{\lambda \; a}\left( \omega_{j} \right)} = {\int{c^{2}\left( {{s_{\lambda \; a}(t)},{{r^{\prime}\left( {\omega_{j},t} \right)}{t}}} \right.}}} \\{= {{{\delta \left( {\omega - \omega_{a}} \right)}{\int{{s_{\lambda \; a}^{2}(t)}{t}}}} + {{\delta \left( {\omega - \omega_{v}} \right)}{\int{{n_{\lambda \; b}^{2}(t)}{{t}.}}}}}}\end{matrix} & \left( {47a} \right)\end{matrix}$

It must be understood that one could, equally well, have chosen themeasured signal S_(λb)(t) as the first input to the correlation cancelerand the plurality of reference signals r′(ω₁, t), r′(ω₂, t), . . . ,r′(ω_(n), t) as the second input. In this event, the correlationcanceler energy output is

$\begin{matrix}\begin{matrix}{{E_{\lambda \; b}\left( \omega_{j} \right)} = {\int{c^{2}\left( {{s_{\lambda \; b}(t)},{{r^{\prime}\left( {\omega,t} \right)}{t}}} \right.}}} \\{= {{{\delta \left( {\omega - r_{a}} \right)}{\int{{s_{\lambda \; b}^{2}(t)}{t}}}} + {{\delta \left( {\omega_{j} - \omega_{v}} \right)}{\int{{n_{\lambda \; b}^{2}(t)}{{t}.}}}}}}\end{matrix} & \left( {47b} \right)\end{matrix}$

It must also be understood that in practical situations the use ofdiscrete time measurement signals may be employed as well as continuoustime measurement signals. In the event that discrete time measurementsignals are used integration approximation methods such as the trapezoidrule, midpoint rule, Tick's rule, Simpson's approximation or othertechniques may be used to compute the correlation canceler energy orpower output. In the discrete time measurement signal case, the energyoutput of the correlation canceler may be written, using the trapezoidrule, as

$\begin{matrix}{{E_{\lambda \; a}(\omega)} = {{{\delta \left( {\omega - \omega_{a}} \right)}\Delta \; t\left\{ {{\sum\limits_{i = 0}^{n}{s_{\lambda \; a}^{2}\left( t_{i} \right)}} - {0.5\left( {{s_{\lambda \; a}^{2}\left( t_{0} \right)} + {s_{\lambda \; a}^{2}\left( t_{n} \right)}} \right)}} \right\}} + {{\delta \left( {\omega - \omega_{v}} \right)}\Delta \; t\left\{ {{\sum\limits_{i = 0}^{n}{n_{\lambda \; a}^{2}\left( t_{i} \right)}} - {0.5\left( {{n_{\lambda \; a}^{2}\left( t_{0} \right)} + {n_{\lambda \; a}^{2}\left( t_{n} \right)}} \right)}} \right\}}}} & \left( {48a} \right) \\{{E_{\lambda \; b}(\omega)} = {{{\delta \left( {\omega - \omega_{a}} \right)}\Delta \; t\left\{ {{\sum\limits_{i = 0}^{n}{s_{\lambda \; b}^{2}\left( t_{i} \right)}} - {0.5\left( {{s_{\lambda \; b}^{2}\left( t_{0} \right)} + {s_{\lambda \; b}^{2}\left( t_{n} \right)}} \right)}} \right\}} + {{\delta \left( {\omega - \omega_{v}} \right)}\Delta \; t\left\{ {{\sum\limits_{i = 0}^{n}{n_{\lambda \; b}^{2}\left( t_{i} \right)}} - {0.5\left( {{n_{\lambda \; b}^{2}\left( t_{0} \right)} + {n_{\lambda \; b}^{2}\left( t_{n} \right)}} \right)}} \right\}}}} & \left( {48b} \right)\end{matrix}$

where t_(i) is the i^(th) discrete time, t₀ is the initial time, t_(n)is the final time and Δt is the time between discrete time measurementsamples.

The energy functions given above, and shown in FIG. 7 b, indicate thatthe correlation canceler output is usually zero due to correlationbetween the measured signal S_(λa)(t) or S_(λb)(t) and many of theplurality of reference signals r′(ω₁, t), r′(ω₂, t), . . . , r′(ω_(n),t)r′(ω, t). However, the energy functions are non zero at values ofω_(j) which correspond to cancellation of either the primary signalportions s_(λa)(t) and s_(λb)(t) or the secondary signal portionsn_(λa)(t) and n_(λb)(t) in the reference signal r′(ω_(j), t). Thesevalues correspond to the signal coefficients ω_(a) and ω_(v).

It must be understood that there may be instances in time when eitherthe primary signal portions s_(λa)(t) and s_(λb)(t) or the secondarysignal portions n_(λa)(t) and n_(λb)(t) are identically zero or nearlyzero. In these cases, only one signal coefficient value will providemaximum energy or power output of the correlation canceler.

Since there may be more than one signal coefficient value which providesmaximum correlation canceler energy or power output, an ambiguity mayarise. It may not be immediately obvious which signal coefficienttogether with the reference function r′(ω, t) provides either theprimary or secondary reference. In such cases, it is necessary toconsider the constraints of the physical system at hand. For example, inpulse oximetry, it is known that arterial blood, whose signature is theprimary plethysmographic wave, has greater oxygen saturation than venousblood, whose signature is the secondary erratic or random signal.Consequently, in pulse oximetry, the ratio of the primary signals due toarterial pulsation ω_(a)=s_(λa)(t)/s_(λb)(t) is the smaller of the twosignal coefficient values while the ratio of the secondary signals dueto mainly venous blood dynamics ω_(v)=n_(λa)(t)/n_(λb)(t) is the largerof the two signal coefficient values, assuming λa=660 nm and λb=940 nm.

It must be understood that in practical implementations of the pluralityof reference signals and cross correlator technique, the ideal featureslisted as properties (1), (2) and (3) above will not be preciselysatisfied but will be approximations thereof. Therefore, in practicalimplementations of the present invention, the correlation cancelerenergy curves depicted in FIG. 7 b will not consist of infinitely narrowdelta functions but will have finite width associated with them asdepicted in FIG. 7 c.

It should also be understood that it is possible to have more than twosignal coefficient values which produce maximum energy or power outputfrom a correlation canceler. This situation will arise when the measuredsignals each contain more than two components each of which are relatedby a ratio as follows:

$\begin{matrix}{{{s_{\lambda \; a}(t)} = {{\sum\limits_{i = 1}^{n}{{f_{{\lambda \; a},i}(t)}{s_{\lambda \; b}(t)}}} = {\sum\limits_{i = 1}^{n}{f_{{\lambda \; b},i}(t)}}}}{where}{{f_{{\lambda \; a},i}(t)} = {\omega \; {f_{{\lambda \; b},i}(t)}}}{{i = 1},\ldots \mspace{14mu},n}{\omega_{i} \neq {\omega_{j}.}}} & (49)\end{matrix}$

The ability to employ reference signal techniques together with acorrelation cancellation, such as an adaptive noise canceler, todecompose a signal into two or more signal components each of which isrelated by a ratio is a further aspect of the present invention.

Preferred Correlation Canceler Using a Joint Process EstimatorImplementation

Once either the secondary reference n′(t) or the primary reference s′(t)is determined by the processor of the present invention using either theabove described ratiometric or constant saturation methods, thecorrelation canceler can be implemented in either hardware or software.The preferred implementation of a correlation canceler is that of anadaptive noise canceler using a joint process estimator.

The least mean squares (LMS) implementation of the internal processor 32described above in conjunction with the adaptive noise canceler of FIG.5 a and FIG. 5 b is relatively easy to implement, but lacks the speed ofadaptation desirable for most physiological monitoring applications ofthe present invention. Thus, a faster approach for adaptive noisecanceling, called a least-squares lattice joint process estimator model,is preferably used. A joint process estimator 60 is showndiagrammatically in FIG. 8 and is described in detail in Chapter 9 ofAdaptive Filter Theory by Simon Haykin, published by Prentice-Hall,copyright 1986. This entire book, including Chapter 9, is herebyincorporated herein by reference. The function of the joint processestimator is to remove either the secondary signal portions n_(λa)(t) orn_(λb)(t) or the primary signal portions s_(λa)(t) or s_(λb)(t) from themeasured signals S_(λa)(t) or S_(λb)(t), yielding either a signals″_(λa)(t) or s″_(λb)(t) or a signal n″_(λa)(t) or n″_(λb)(t) which is agood approximation to either the primary signal s_(λa)(t) or s_(λb)(t)or the secondary signal n_(λa)(t) or n_(λb)(t). Thus, the joint processestimator estimates either the value of the primary signals s_(λa)(t) ors_(λb)(t) or the secondary signals n_(λa)(t) or n_(λb)(t). The inputs tothe joint process estimator 60 are either the secondary reference n′(t)or the primary reference s′(t) and the composite measured signalS_(λa)(t) or S_(λb)(t). The output is a good approximation to the signalS_(λa)(t) or S_(λb)(t) with either the secondary signal or the primarysignal removed, i.e. a good approximation to either s_(λa)(t),s_(λb)(t), n_(λa)(t) or n_(λb)(t).

The joint process estimator 60 of FIG. 8 utilizes, in conjunction, aleast square lattice predictor 70 and a regression filter 80. Either thesecondary reference n′(t) or the primary reference s′(t) is input to theleast square lattice predictor 70 while the measured signal S_(λa)(t) orS_(λb)(t) is input to the regression filter 80. For simplicity in thefollowing description, S_(λa)(t) will be the measured signal from whicheither the primary portion s_(λa)(t) or the secondary portion n_(λa)(t)will be estimated by the joint process estimator 60. However, it will benoted that S_(λb)(t) could equally well be input to the regressionfilter 80 and the primary portion s_(λb)(t) or the secondary portionn_(λb)(t) of this signal could equally well be estimated.

The joint process estimator 60 removes all frequencies that are presentin both the reference n′(t) or s′(t), and the measured signal S_(λa)(t).The secondary signal portion n_(λa)(t) usually comprises frequenciesunrelated to those of the primary signal portion s_(λa)(t). It is highlyimprobable that the secondary signal portion n_(λa)(t) would be ofexactly the same spectral content as the primary signal portions_(λa)(t). However, in the unlikely event that the spectral contents_(λa)(t) and n_(λa)(t) are similar, this approach will not yieldaccurate results. Functionally, the joint process estimator 60 comparesthe reference input signal n′(t) or s′(t), which is correlated to eitherthe secondary signal portion n_(λa)(t) or the primary signal portions_(λa)(t), and input signal S_(λa)(t) and removes all frequencies whichare identical. Thus, the joint process estimator 60 acts as a dynamicmultiple notch filter to remove those frequencies in the secondarysignal component n_(λa)(t) as they change erratically with the motion ofthe patient or those frequencies in the primary signal components_(λa)(t) as they change with the arterial pulsation of the patient.This yields a signal having substantially the same spectral content andamplitude as either the primary signal s_(λa)(t) or the secondary signaln_(λa)(t). Thus, the output s″_(λa)(t) or n″_(λa)(t) of the jointprocess estimator 60 is a very good approximation to either the primarysignal s_(λa)(t) or the secondary signal n_(λa)(t). The joint processestimator 60 can be divided into stages, beginning with a zero-stage andterminating in an m^(th)-stage, as shown in FIG. 8. Each stage, exceptfor the zero-stage, is identical to every other stage. The zero-stage isan input stage for the joint process estimator 60. The first stagethrough the m^(th)-stage work on the signal produced in the immediatelyprevious stage, i.e., the (_(m−1))^(th)-stage, such that a goodapproximation to either the primary signal s″_(λa)(t) or the secondarysignal n″_(λa)(t) is produced as output from the m^(th)-stage.

The least-squares lattice predictor 70 comprises registers 90 and 92,summing elements 100 and 102, and delay elements 110. The registers 90and 92 contain multiplicative values of a forward reflection coefficientΓ_(f,m)(t) and a backward reflection coefficient Γ_(b,m)(t) whichmultiply the reference signal n′(t) or s′(t) and signals derived fromthe reference signal n′(t) or s′(t). Each stage of the least-squareslattice predictor outputs a forward prediction error f_(m)(t) and abackward prediction error b_(m)(t). The subscript m is indicative of thestage.

For each set of samples, i.e. one sample of the reference signal n′(t)or s′(t) derived substantially simultaneously with one sample of themeasured signal S_(λa)(t), the sample of the reference signal n′(t) ors′(t) is input to the least-squares lattice predictor 70. The zero-stageforward prediction error f₀(t) and the zero-stage backward predictionerror b₀(t) are set equal to the reference signal n′(t) or s′(t). Thebackward prediction error b₀(t) is delayed by one sample period by thedelay element 110 in the first stage of the least-squares latticepredictor 70. Thus, the immediately previous value of the referencen′(t) or s′(t) is used in calculations involving the first-stage delayelement 110. The zero-stage forward prediction error is added to thenegative of the delayed zero-stage backward prediction error b₀(t−1)multiplied by the forward reflection coefficient value Γ_(f,1)(t)register 90 value, to produce a first-stage forward prediction errorf₁(t). Additionally, the zero-stage forward prediction error f₀(t) ismultiplied by the backward reflection coefficient value Γ_(b,1)(t)register 92 value and added to the delayed zero-stage backwardprediction error b₀(t−1) to produce a first-stage backward predictionerror b₁(t). In each subsequent stage, m, of the least square latticepredictor 70, the previous forward and backward prediction error values,f_(m−1)(t) and b_(m−1)(t−1), the backward prediction error being delayedby one sample period, are used to produce values of the forward andbackward prediction errors for the present stage, f_(m)(t) and b_(m)(t).

The backward prediction error b_(m)(t) is fed to the concurrent stage,m, of the regression filter 80. There it is input to a register 96,which contains a multiplicative regression coefficient valueκ_(m,λa)(t). For example, in the zero-stage of the regression filter 80,the zero-stage backward prediction error b₀(t) is multiplied by thezero-stage regression coefficient κ_(0,λa)(t) register 96 value andsubtracted from the measured value of the signal S_(λa)(t) at a summingelement 106 to produce a first stage estimation error signale_(1,λa)(t). The first-stage estimation error signal e_(1,λa)(t) is afirst approximation to either the primary signal or the secondarysignal. This first-stage estimation error signal e_(1,λa)(t) is input tothe first-stage of the regression filter 80. The first-stage backwardprediction error b₁(t), multiplied by the first-stage regressioncoefficient κ_(1,λa)(t) register 96 value is subtracted from thefirst-stage estimation error signal e_(1,λa)(t) to produce thesecond-stage estimation error e_(2,λa)(t). The second-stage estimationerror signal e_(2,λa)(t) is a second, somewhat better approximation toeither the primary signal s_(λa)(t) or the secondary signal n_(λa)(t).

The same processes are repeated in the least-squares lattice predictor70 and the regression filter 80 for each stage until a goodapproximation e_(m,λa)(t), to either the primary signal s_(λa)(t) or thesecondary signal n_(λa)(t) is determined. Each of the signals discussedabove, including the forward prediction error f_(m)(t), the backwardprediction error b_(m)(t), the estimation error signal e_(m,λa)(t), isnecessary to calculate the forward reflection coefficient Γ_(f,m)(t),the backward reflection coefficient Γ_(b,m)(t), and the regressioncoefficient κ_(m,λa)(t) register 90, 92, and 96 values in each stage, m.In addition to the forward prediction error f_(m)(t), the backwardprediction error b_(m)(t), and the estimation error e_(m,λa)(t) signals,a number of intermediate variables, not shown in FIG. 8 but based on thevalues labeled in FIG. 8, are required to calculate the forwardreflection coefficient Γ_(f,m)(t) the backward reflection coefficientΓ_(b,m)(t), and the regression coefficient κ_(m,λa)(t) register 90,92,and 96 values.

Intermediate variables include a weighted sum of the forward predictionerror squares J_(m)(t), a weighted sum of the backward prediction errorsquares β_(m)(t), a scalar parameter Δ_(m)(t), a conversion factorγ_(m)(t), and another scalar parameter ρ_(m,λa)(t). The weighted sum ofthe forward prediction errors J_(m)(t) is defined as:

m  ( t ) = ∑ i = 1 t  λ t - i   f m  ( i )  2 ; ( 50 )

where λ without a wavelength identifier, a or b, is a constantmultiplicative value unrelated to wavelength and is typically less thanor equal to one, i.e., λ≦1. The weighted sum of the backward predictionerrors β_(m)(t) is defined as:

$\begin{matrix}{{\beta_{m}(t)} = {\sum\limits_{i = 1}^{t}{\lambda^{t = i}{{b_{m}(i)}}^{2}}}} & (51)\end{matrix}$

where, again, λ without a wavelength identifier, a or b, is a constantmultiplicative value unrelated to wavelength and is typically less thanor equal to one, i.e., λ≦1. These weighted sum intermediate errorsignals can be manipulated such that they are more easily solved for, asdescribed in Chapter 9, §9.3. and defined hereinafter in equations (65)and (66).

Description of the Joint Process Estimator

The operation of the joint process estimator 60 is as follows. When thejoint process estimator 60 is turned on, the initial values ofintermediate variables and signals including the parameter Δ_(m−1)(t),the weighted sum of the forward prediction error signals J_(m−1)(t), theweighted sum of the backward prediction error signals β_(m−1)(t), theparameter ρ_(m,λa)(t), and the zero-stage estimation error e_(0,λa)(t)are initialized, some to zero and some to a small positive number δ:

Δ_(m−1)(0)=0;  (52)

_(m−1)(0)=6;  (53)

β_(m−1)(0)=6;  (54)

ρ_(m,λa)(0)=0;  (55)

e _(0,λa)(t)=S _(λa)(t) for t≧0.  (56)

After initialization, a simultaneous sample of the measured signalS_(λa)(t) or S_(λb)(t) and either the secondary reference n′(t) or theprimary reference s′(t) are input to the joint process estimator 60, asshown in FIG. 8. The forward and backward prediction error signals f₀(t)and b₀(t), and intermediate variables including the weighted sums of theforward and backward error signals J₀(t) and β₀(t), and the conversionfactor γ₀(t) are calculated for the zero-stage according to:

f ₀(t)=b ₀(t)=n′(t)  (57a)

J ₀(t)=β₀(t)=λJ ₀(t−1)+|n′(t)|²  (58a)

γ₀(t−1)=1  (59a)

if a secondary reference n′(t) is used or according to:

f ₀(t)=b ₀(t)=s′(t)  (57b)

J ₀(t)=β₀(t)=λJ ₀(t−1)+|s′(t)|²  (58b)

β₀(t−1)=1  (59b)

if a primary reference s′(t) is used where, again, λ without awavelength identifier, a or b, is a constant multiplicative valueunrelated to wavelength.

Forward reflection coefficient Γ_(f,m)(t), backward reflectioncoefficient Γ_(b,m)(t), and regression coefficient κ_(m,λa)(t) register90, 92 and 96 values in each stage thereafter are set according to theoutput of the previous stage. The forward reflection coefficientΓ_(f,1)(t), backward reflection coefficient Γ_(b,1)(t), and regressioncoefficient κ_(1,λa)(t) register 90, 92 and 96 values in the first stageare thus set according to algorithm using values in the zero-stage ofthe joint process estimator 60. In each stage, m≧1, intermediate valuesand register values including the parameter Δ_(m−1)(t); the forwardreflection coefficient Γ_(f,m)(t) register 90 value; the backwardreflection coefficient Γ_(b,m)(t) register 92 value; the forward andbackward error signals f_(m)(t) and b_(m)(t); the weighted sum ofsquared forward prediction errors J_(f,m)(t), as manipulated in §9.3 ofthe Haykin book; the weighted sum of squared backward prediction errorsβ_(b),m(t), as manipulated in §9.3 of the Haykin book; the conversionfactor γ_(m)(t); the parameter ρ_(m,λa)(t); the regression coefficientκ_(m,λa)(t) register 96 value; and the estimation error e_(m+1λa)(t)value are set according to:

Δ_(m−1)(t)=λΔ_(m−1)(t−1)+{b _(m−1)(t−1)f* _(m−1)(t)/γ_(m−1)(t−1)}  (60)

Γ_(f,m)(t)=−{Δ_(m−1)(t)/β_(m−1)(t−1)}  (61)

Γ_(b,m)(t)=−{Δ*_(m−1)(t)/J _(m−1)(t)}  (62)

f _(m)(t)=f _(m−1)(t)+Γ*_(f,m)(t)b _(m−1)(t−1)  (63)

b _(m)(t)=b _(m−1)(t−1)+Γ*_(b,m)(t)f _(m−1)(t)  (64)

J _(m)(t)=J _(m−1)(t)−{|Δ_(m−1)(t)|²/β_(m−1)(t−1)}  (65)

β_(m)(t)=β_(m−1)(t−1)−{|Δ_(m−1)(t)|² /J _(m−1)(t)}  (66)

γ_(m)(t−1)=γ_(m−1)(t−1)−{|b _(m−1)(t−1)|²/β_(m−1)(t−1)}  (67)

ρ_(m,λa)(t)=λρ_(m,λa)(t−1)+{b _(m)(t)ε*_(m,λa)(t)/γ_(m)(t)}  (68)

κ_(m,λa)(t)={ρ_(m,λa)(t)/β_(m)(t)}  (69)

ε_(m+1,λa)(t)=ε_(m,λa)(t)−κ*_(m)(t)b _(m)(t)  (70)

where a(*) denotes a complex conjugate.

These equations cause the error signals f_(m)(t), b_(m)(t), e_(m,λa)(t)to be squared or to be multiplied by one another, in effect squaring theerrors, and creating new intermediate error values, such as Δ_(m)−1(t).The error signals and the intermediate error values are recursively tiedtogether, as shown in the above equations (60) through (70). Theyinteract to minimize the error signals in the next stage.

After a good approximation to either the primary signal s_(λa)(t) or thesecondary signal n_(λa)(t) has been determined by the joint processestimator 60, a next set of samples, including a sample of the measuredsignal S_(λa)(t) and a sample of either the secondary reference n′(t) orthe primary reference s′(t), are input to the joint process estimator60. The re-initialization process does not reoccur, such that theforward and backward reflection coefficient Γ_(f),m(t) and Γ_(b),m(t)register 90, 92 values and the regression coefficient κ_(m,λa)(t)register 96 value reflect the multiplicative values required to estimateeither the primary signal portion s_(λa)(t) or the secondary signalportion n_(λa)(t) of the sample of S_(λa)(t) input previously. Thus,information from previous samples is used to estimate either the primaryor secondary signal portion of a present set of samples in each stage.

Flowchart of Joint Process Estimator

In a signal processor, such as a physiological monitor, incorporating areference processor of the present invention to determine a referencen′(t) or s′(t) for input to a correlation canceler, a joint processestimator 60 type adaptive noise canceler is generally implemented via asoftware program having an iterative loop. One iteration of the loop isanalogous to a single stage of the joint process estimator as shown inFIG. 8. Thus, if a loop is iterated m times, it is equivalent to an mstage joint process estimator 60.

A flow chart of a subroutine to estimate the primary signal portions_(λa)(t) or the secondary signal portion n_(λa)(t) of a measuredsignal, S_(λa)(t) is shown in FIG. 9. The flow chart describes how theaction of a reference processor for determining either the secondaryreference or the primary reference and the joint process estimator 60would be implemented in software.

A one-time only initialization is performed when the physiologicalmonitor is turned on, as indicated by an “INITIALIZE NOISE CANCELER” box120. The initialization sets all registers 90, 92, and 96 and delayelement variables 110 to the values described above in equations (52)through (56).

Next, a set of simultaneous samples of the measured signals S_(λa)(t)and S_(λb)(t) is input to the subroutine represented by the flowchart inFIG. 9. Then a time update of each of the delay element programvariables occurs, as indicated in a “TIME UPDATE OF [Z⁻¹] ELEMENTS” box130, wherein the value stored in each of the delay element variables 110is set to the value at the input of the delay element variable 110.Thus, the zero-stage backward prediction error b₀(t) is stored in thefirst-stage delay element variable, the first-stage backward predictionerror b₁(t) is stored in the second-stage delay element variable, and soon.

Then, using the set of measured signal samples S_(λa)(t) and S_(λb)(t),the reference signal is calculated according to the ratiometric or theconstant saturation method described above. This is indicated by a“CALCULATE REFERENCE [n′(t) or s′(t)] FOR TWO MEASURED SIGNAL SAMPLES”box 140.

A zero-stage order update is performed next as indicated in a“ZERO-STAGE UPDATE” box 150. The zero-stage backward prediction errorb₀(t), and the zero-stage forward prediction error f₀(t) are set equalto the value of the reference signal n′(t) or s′(t). Additionally, theweighted sum of the forward prediction errors J_(m)(t) and the weightedsum of backward prediction errors β_(m)(t) are set equal to the valuedefined in equations (53) and (54).

Next, a loop counter, m, is initialized as indicated in a “m=0” box 160.A maximum value of m, defining the total number of stages to be used bythe subroutine corresponding to the flowchart in FIG. 9, is alsodefined. Typically, the loop is constructed such that it stops iteratingonce a criterion for convergence upon a best approximation to either theprimary signal or the secondary signal has been met by the joint processestimator 60. Additionally, a maximum number of loop iterations may bechosen at which the loop stops iteration. In a preferred embodiment of aphysiological monitor of the present invention, a maximum number ofiterations, m=6 to m=10, is advantageously chosen.

Within the loop, the forward and backward reflection coefficientΓ_(f,m)(t) and Γ_(b,m)(t) register 90 and 92 values in the least-squareslattice filter are calculated first, as indicated by the “ORDER UPDATEMTH CELL OF LSL-LATTICE” box 170 in FIG. 9. This requires calculation ofintermediate variable and signal values used in determining register 90,92, and 96 values in the present stage, the next stage, and in theregression filter 80.

The calculation of regression filter register 96 value κ_(m,λa)(t) isperformed next, indicated by the “ORDER UPDATE MTH STAGE OF REGRESSIONFILTER(S)” box 180. The two order update boxes 170 and 180 are performedin sequence m times, until m has reached its predetermined maximum (inthe preferred embodiment, m=6 to m=10) or a solution has been convergedupon, as indicated by a YES path from a “DONE” decision box 190. In acomputer subroutine, convergence is determined by checking if theweighted sums of the forward and backward prediction errors J_(m)(t) andβ_(m)(t) are less than a small positive number. An output is calculatednext, as indicated by a “CALCULATE OUTPUT” box 200. The output is a goodapproximation to either the primary signal or secondary signal, asdetermined by the reference processor 26 and joint process estimator 60subroutine corresponding to the flow chart of FIG. 9. This is displayed(or used in a calculation in another subroutine), as indicated by a “TODISPLAY” box 210.

A new set of samples of the two measured signals S_(λa)(t) and S_(λb)(t)is input to the processor and joint process estimator 60 adaptive noisecanceler subroutine corresponding to the flowchart of FIG. 9 and theprocess reiterates for these samples. Note, however, that theinitialization process does not re-occur. New sets of measured signalsamples S_(λa)(t) and S_(λb)(t) are continuously input to the referenceprocessor 26 and joint process estimator 60 adaptive noise cancelersubroutine. The output forms a chain of samples which is representativeof a continuous wave. This waveform is a good approximation to eitherthe primary signal waveform s_(λa)(t) or the secondary waveformn_(λa)(t) at wavelength λa. The waveform may also be a goodapproximation to either the primary signal waveform s_(λb)(t) or thesecondary waveform n″_(λb)(t) at wavelength λb.

Calculation of Saturation from Correlation Canceler Output

Physiological monitors may use the approximation of the primary signalss″_(λa)(t) or s″_(λb)(t) or the secondary signals n″_(λa)(t) orn″_(λb)(t) to calculate another quantity, such as the saturation of oneconstituent in a volume containing that constituent plus one or moreother constituents. Generally, such calculations require informationabout either a primary or secondary signal at two wavelengths. Forexample, the constant saturation method requires a good approximation ofthe primary signal portions s_(λa)(t) and s_(λb)(t) of both measuredsignals S_(λa)(t) and S_(λb)(t) Then, the arterial saturation isdetermined from the approximations to both signals, i.e. s″_(λa)(t) ands″_(λb)(t). The constant saturation method also requires a goodapproximation of the secondary signal portions n_(λa)(t) or n_(λb)(t).Then an estimate of the venous saturation may be determined from theapproximations to these signals i.e. n″_(λa)(t) and n″_(λb)(t).

In other physiological measurements, information about a signal at athird wavelength is necessary. For example, to find the saturation usingthe ratiometric method, signals S_(λa)(t) and S_(λb)(t) are used to findthe reference signal n′(t) or s′(t). But as discussed previously, λa andλb were chosen to satisfy a proportionality relationship like that ofequation (22). This proportionality relationship forces the two primarysignal portions s_(λa)(t) and s_(λb)(t) of equations (23c) and (24c) tobe linearly dependent. Generally, linearly dependent mathematicalequations cannot be solved for the unknowns. Analogously, some desirableinformation cannot be derived from two linearly dependent signals. Thus,to determine the saturation using the ratiometric method, a third signalis simultaneously measured at wavelength λc. The wavelength λc is chosensuch that the primary portion s_(λc)(t) of the measured signal S_(λc)(t)is not linearly dependent with the primary portions s_(λa)(t) ands_(λb)(t) of the measured signals S_(λa)(t) and S_(λb)(t). Since allmeasurements are taken substantially simultaneously, the secondaryreference signal n′(t) is correlated to the secondary signal portionsn_(λa), n_(λb), and n _(λc) of each of the measured signals S_(λa)(t),S_(λb)(t), and S_(λc)(t) and can be used to estimate approximations tothe primary signal portions s_(λa)(t), s_(λb)(t), and s_(λc)(t) for allthree measured signals S_(λa)(t), S_(λb)(t), and S_(λc)(t). Using theratiometric method, estimation of the ratio of signal portions s_(λa)(t)and s_(λc)(t) of the two measured signals S_(λa)(t) and S_(λc)(t),chosen correctly, is usually satisfactory to determine mostphysiological data.

A joint process estimator 60 having two regression filters 80 a and 80 bis shown in FIG. 10. A first regression filter 80 a accepts a measuredsignal S_(λa)(t). A second regression filter 80 b accepts a measuredsignal S_(λb)(t) or S_(λc)(t), depending whether the constant saturationmethod or the ratiometric method is used to determine the referencesignal n′(t) or s′(t) for the constant saturation method or. n′(t) ors′(t) for the ratiometric method. The first and second regressionfilters 80 a and 80 b are independent. The backward prediction errorb_(m)(t) is input to each regression, filter 80 a and 80 b, the inputfor the second regression filter 80 b bypassing the first regressionfilter 80 a.

The second regression filter 80 b comprises registers 98, and summingelements 108 arranged similarly to those in the first regression filter80 a. The second regression filter 80 b operates via an additionalintermediate variable in conjunction with those defined by equations(60) through (70), i.e.:

ρ_(m,λb)(t)=λρ_(m,λb)(t−1)+{b _(m)(t)e* _(m,λb)(t)/γ_(m)(t)}; or  (71)

ρ_(m,λc)(t)=λρ_(m,λc)(t−1)+{b _(m)(t)e* _(m,λc)(t)/γ_(m)(t)}; and  (72)

ρ_(0,λb)(0)=0; or  (73)

ρ_(0,λc)(0)=0.  (74)

The second regression filter 80 b has an error signal value definedsimilar to the first regression filter error signal values,e_(m+1,λa)(t), i.e.:

e _(m+1,λb)(t)=e _(m,λb)(t)−κ*_(m,λb)(t)b _(m)(t); or  (75)

e _(m+1,λc)(t)=e _(m,λc)(t)−κ*_(m,λb)(t)b _(m)(t); and  (76)

e _(0,λb)(t)=S _(λb)(t) for t≧0; or  (77)

e _(0,λc)(t)=S _(λc)(t) for t≧0.  (78)

The second regression filter has a regression coefficient κ_(m,λb)(t)register 98 value defined similarly to the first regression filter errorsignal values, i.e.:

κ_(m,λb)(t)={ρ_(m,λb)(t)/β_(m)(t)}; or  (79)

κ_(m,λc)(t)={ρ_(m,λc)(t)/β_(m)(t)}.  (80)

These values are used in conjunction with those intermediate variablevalues, signal values, register and register values defined in equations(52) through (70). These signals are calculated in an order defined byplacing the additional signals immediately adjacent a similar signal forthe wavelength λa.

For the ratiometric method, S_(λc)(t) is input to the second regressionfilter 80 b. The output of the second regression filter 80 b is then agood approximation to the primary signal s″_(λc)(t) or secondary signaln″_(λc)(t). For the constant saturation method, S_(λb)(t) is input tothe second regression filter 80 b. The output is then a goodapproximation to the primary signal s″_(λb)(t) or secondary signals″_(λb)(t).

The addition of the second regression filter 80 b does not substantiallychange the computer program subroutine represented by the flowchart ofFIG. 9. Instead of an order update of the m^(th) in stage of only oneregression filter, an order update of the m^(th) stage of bothregression filters 80 a and 80 b is performed. This is characterized bythe plural designation in the “ORDER UPDATE OF min STAGE OF REGRESSIONFILTER(S)” box 180 in FIG. 9. Since the regression filters 80 a and 80 boperate independently, independent calculations can be performed in thereference processor and joint process estimator 60 adaptive noisecanceler subroutine modeled by the flowchart of FIG. 9.

Calculation of Saturation

Once good approximations to the primary signal portions, s″_(λa)(t) ands″_(λc)(t) or the secondary signal portions n″_(λa)(t) and n″_(λc)(t)for the ratiometric method and s″_(λa)(t) and s″_(λb)(t) or n″_(λa)(t)and n″_(λc)(t) for the constant saturation method, have been determinedby the joint process estimator 60, the saturation of A₅ in a volumecontaining A₅ and A₆, for example, may be calculated according tovarious known methods. Mathematically, the approximations to the primarysignals can be written:

s″ _(λa)(t)≈ε_(5,λa) c ₅ x _(5,6)(t)+ε_(6,λa) c ₆ x _(5,6)(t)+ε_(5,λa) c₃ x _(3,4)(t)+ε_(6,λa) c ₃ x _(3,4)(t)  (81a)

s″ _(λc)(t)≈ε_(5,λc) c ₅ x _(5,6)(t)+ε_(6,λc) c ₆ x _(5,6)(t)+ε_(5,λc) c₃ x _(3,4)(t)+ε_(6,λc) c ₃ x _(3,4)(t)  (82a)

for the ratiometric method using wavelengths λa and λc, and assumingthat the secondary reference n′(t) is uncorrelated with x_(3,4)(t) andx_(5,6)(t). Terms involving x_(3,4)(t) and x₅,6(t) may then be separatedusing the constant saturation method. It is important to understand thatif n′(t) is uncorrelated with x_(3,4)(t) and x_(5,6)(t), use of theratiometric method followed by use of the constant saturation methodresults in a more accurate computation of the saturation of A₃ in thelayer x_(3,4) then by use of the ratiometric or constant saturationmethods alone. In the event that n′(t) and x_(3,4)(t) are correlated theratiometric method yields

s″ _(λa)(t)≈ε_(5,λc) c ₅ x _(5,6)(t)+ε_(6,λa) c ₆ x _(5,6)(t);and  (81b)

s″ _(λc)(t)≈ε_(5,λc) c ₅ x _(5,6)(t)+ε_(6,λc) c ₆ x _(5,6)(t).  (82b)

For the constant saturation method, the approximations to the primarysignals can be written, in terms of λa and λb, as:

s″ _(λa)(t)≈ε_(5,λa) c ₅ x _(5,6)(t)+ε_(6,λc) c ₆ x _(5,6)(t); and  (83)

s″ _(λb)(t)≈ε_(5,λb) c ₅ x _(5,6)(t)+ε_(6,λb) c ₆ x _(5,6)(t).  (84)

Equations (81b), (82b), (83) and (84) are equivalent to two equationshaving three unknowns, namely c₅(t), c₆(t) and x₅,6(t). In both theratiometric and the constant saturation cases, the saturation can bedetermined by acquiring approximations to the primary or secondarysignal portions at two different, yet proximate times t₁ and t₂ overwhich the saturation of A₅ in the volume containing A₅ and A₆ and thesaturation of A₃ in the volume containing A₃ and A₄ does not changesubstantially. For example, for the primary signals estimated by theratiometric method, at times t₁ and t₂:

s″ _(λa)(t ₁)≈ε_(5,λa) c ₅ x _(5,6)(t ₁)+ε_(6,λa) c ₆ x _(5,6)(t₁)  (85)

s″ _(λc)(t ₁)≈ε_(5,λc) c ₅ x _(5,6)(t ₁)+ε_(6,λc) c ₆ x _(5,6)(t₁)  (86)

s″ _(λa)(t ₂)≈ε_(5,λa) c ₅ x _(5,6)(t ₂)+ε_(6,λa) c ₆ x _(5,6)(t₂)  (87)

s″ _(λc)(t ₂)≈ε_(5,λc) c ₅ x _(5,6)(t ₂)+ε_(6,λc) c ₆ x _(5,6)(t₂)  (88)

Then, difference signals may be determined which relate the signals ofequations (85) through (88), i.e.:

Δs _(λa) =s″ _(λa)(t ₁)−s″ _(λa)(t ₂)≈ε_(5,λa) c ₅ Δx+ε _(6,λa) c ₆ Δx;and  (89)

Δs _(λc) =s″ _(λc)(t ₁)−s″ _(λc)(t ₂)≈ε_(5,λc) c ₅ Δx+ε _(,λc) c ₆Δx.  (90)

where Δx=x_(5,6)(t₁)−x_(5,6)(t₂). The average saturation at timet=(t₁+t₂)/2 is:

$\begin{matrix}{{{Saturation}(t)} = {{c_{5}(t)}/\left\lbrack {{c_{5}(t)} + {c_{6}(t)}} \right\rbrack}} & (91) \\{\mspace{135mu} {= \frac{ɛ_{6,{\lambda \; a}} - {ɛ_{6,{\lambda \; c}}\left( {\Delta \; {s_{\lambda \; a}/\Delta}\; s_{\lambda \; c}} \right)}}{ɛ_{6,{\lambda \; a}} - ɛ_{5,{\lambda \; a}} - {\left( {ɛ_{6,{\lambda \; a}} - ɛ_{5,{\lambda \; a}}} \right)\left( {\Delta \; {s_{\lambda \; a}/\Delta}\; s_{\lambda \; c}} \right)}}}} & (92)\end{matrix}$

It will be understood that the Δx term drops out from the saturationcalculation because of the division. Thus, knowledge of the thickness ofthe primary constituents is not required to calculate saturation.

Pulse Oximetry Measurements

A specific example of a physiological monitor utilizing a processor ofthe present invention to determine a secondary reference n′(t) for inputto a correlation canceler that removes erratic motion-induced secondarysignal portions is a pulse oximeter. Pulse oximetry may also beperformed utilizing a processor of the present invention to determine aprimary signal reference s′(t) which may be used for display purposes orfor input to a correlation canceler to derive information about patientmovement and venous blood oxygen saturation.

A pulse oximeter typically causes energy to propagate through a mediumwhere blood flows close to the surface for example, an ear lobe, or adigit such as a finger, or a forehead. An attenuated signal is measuredafter propagation through or reflected from the medium. The pulseoximeter estimates the saturation of oxygenated blood.

Freshly oxygenated blood is pumped at high pressure from the heart intothe arteries for use by the body. The volume of blood in the arteriesvaries with the heartbeat, giving rise to a variation in absorption ofenergy at the rate of the heartbeat, or the pulse.

Oxygen depleted, or deoxygenated, blood is returned to the heart by theveins along with unused oxygenated blood. The volume of blood in theveins varies with the rate of breathing, which is typically much slowerthan the heartbeat. Thus, when there is no motion induced variation inthe thickness of the veins, venous blood causes a low frequencyvariation in absorption of energy. When there is motion inducedvariation in the thickness of the veins, the low frequency variation inabsorption is coupled with the erratic variation in absorption due tomotion artifact.

In absorption measurements using the transmission of energy through amedium, two light emitting diodes (LED's) are positioned on one side ofa portion of the body where blood flows close to the surface, such as afinger, and a photodetector is positioned on the opposite side of thefinger. Typically, in pulse oximetry measurements, one LED emits avisible wavelength, preferably red, and the other LED emits an infraredwavelength. However, one skilled in the art will realize that otherwavelength combinations could be used.

The finger comprises skin, tissue, muscle, both arterial blood andvenous blood, fat, etc., each of which absorbs light energy differentlydue to different absorption coefficients, different concentrations, anddifferent thicknesses. When the patient is not moving, absorption issubstantially constant except for the flow of blood. The constantattenuation can be determined and subtracted from the signal viatraditional filtering techniques. When the patient moves, the absorptionbecomes erratic. Erratic motion induced noise typically cannot bepredetermined and/or subtracted from the measured signal via traditionalfiltering techniques. Thus, determining the oxygen saturation ofarterial blood and venous blood becomes more difficult.

A schematic of a physiological monitor for pulse oximetry is shown inFIG. 11. Two LED's 300 and 302, one LED 300 emitting red wavelengths andanother LED 302 emitting infrared wavelengths, are placed adjacent afinger 310. A photodetector 320, which produces an electrical signalcorresponding to the attenuated visible and infrared light energysignals is located opposite the LED's 300 and 302. The photodetector 320is connected to a single channel of common processing circuitryincluding an amplifier 330 which is in turn connected to a band passfilter 340. The band pass filter 340 passes it output signal into asynchronized demodulator 350 which has a plurality of output channels.One output channel is for signals corresponding to visible wavelengthsand another output channel is for signals corresponding to infraredwavelengths.

The output channels of the synchronized demodulator for signalscorresponding to both the visible and infrared wavelengths are eachconnected to separate paths, each path comprising further processingcircuitry. Each path includes a DC offset removal element 360 and 362,such as a differential amplifier, a programmable gain amplifier 370 and372 and a low pass filter 380 and 382. The output of each low passfilter 380 and 382 is amplified in a second programmable gain amplifier390 and 392 and then input to a multiplexer 400.

The multiplexer 400 is connected to an analog-to-digital converter 410which is in turn connected to a microprocessor 420. Control linesbetween the microprocessor 420 and the multiplexer 400, themicroprocessor 420 and the analog-to-digital converter 410, and themicroprocessor 420 and each programmable gain amplifier 370, 372, 390,and 392 are formed. The microprocessor 420 has additional control lines,one of which leads to a display 430 and the other of which leads to anLED driver 440 situated in a feedback loop with the two LED's 300 and302.

The LED's 300 and 302 each emits energy which is absorbed by the finger310 and received by the photodetector 320. The photodetector 320produces an electrical signal which corresponds to the intensity of thelight energy striking the photodetector 320 surface. The amplifier 330amplifies this electrical signal for ease of processing. The band passfilter 340 then removes unwanted high and low frequencies. Thesynchronized demodulator 350 separates the electrical signal intoelectrical signals corresponding to the red and infrared light energycomponents. A predetermined reference voltage, V_(ref), is subtracted bythe DC offset removal element 360 and 362 from each of the separatesignals to remove substantially constant absorption which corresponds toabsorption when there is no motion induced signal component. Then thefirst programmable gain amplifiers 370 and 372 amplify each signal forease of manipulation. The low pass filters 380 and 382 integrate eachsignal to remove unwanted high frequency components and the secondprogrammable gain amplifiers 390 and 392 amplify each signal for furtherease of processing.

The multiplexer 400 acts as an analog switch between the electricalsignals corresponding to the red and the infrared light energy, allowingfirst a signal corresponding to the red light to enter theanalog-to-digital converter 410 and then a signal corresponding to theinfrared light to enter the analog-to-digital converter 410. Thiseliminates the need for multiple analog-to-digital converters 410. Theanalog-to-digital converter 410 inputs the data into the microprocessor420 for calculation of either a primary or secondary reference signalvia the processing technique of the present invention and removal orderivation of motion induced signal portions via a correlation canceler,such as an adaptive noise canceler. The microprocessor 420 centrallycontrols the multiplexer 400, the analog-to-digital converter 410, andthe first and second programmable gain amplifiers 370 and 390 for boththe red and the infrared channels. Additionally, the microprocessor 420controls the intensity of the. LED's 302 and 304 through the LED driver440 in a servo loop to keep the average intensity received at thephotodetector 320 within an appropriate range. Within the microprocessor420 a reference signal n′(t) or s′(t) is calculated via either theconstant saturation method or the ratiometric method, as describedabove, the constant saturation method being generally preferred. Thissignal is used in an adaptive noise canceler of the joint processestimator type 60, as described above.

The multiplexer 400 time multiplexes, or sequentially switches between,the electrical signals corresponding to the red and the infrared lightenergy. This allows a single channel to be used to detect and beginprocessing the electrical signals. For example, the red LED 300 isenergized first and the attenuated signal is measured at thephotodetector 320. An electrical signal corresponding to the intensityof the attenuated red light energy is passed to the common processingcircuitry. The infrared LED 302 is energized next and the attenuatedsignal is measured at the photodetector 320. An electrical signalcorresponding to the intensity of the attenuated infrared light energyis passed to the common processing circuitry. Then, the red LED 300 isenergized again and the corresponding electrical signal is passed to thecommon processing circuitry. The sequential energization of LED's 300and 302 occurs continuously while the pulse oximeter is operating.

The processing circuitry is divided into distinct paths after thesynchronized demodulator 350 to ease time constraints generated by timemultiplexing. In the preferred embodiment of the pulse oximeter shown inFIG. 11, a sample rate, or LED energization rate, of 625 Hz isadvantageously employed. Thus, electrical signals reach the synchronizeddemodulator 350 at a rate of 625 Hz. Time multiplexing is not used inplace of the separate paths due to settling time constraints of the lowpass filters 380, 382, and 384.

In FIG. 11, a third LED 304 is shown adjacent the finger, located nearthe LED's 300 and 302. The third LED 304 is used to measure a thirdsignal S_(λc)(t) to be used to determine saturation using theratiometric method. The third LED 304 is time multiplexed with the redand infrared LED's 300 and 302. Thus, a third signal is input to thecommon processing circuitry in sequence with the signals from the redand infrared LED's 300 and 302. After passing through and beingprocessed by the operational amplifier 330, the band pass filter 340,and the synchronized demodulator 350, the third electrical signalcorresponding to light energy at wavelength λc is input to a separatepath including a DC offset removal element 364, a first programmablegain amplifier 374, a low pass filter 384, and a second programmablegain amplifier 394. The third signal is then input to the multiplexer400.

The dashed line connection for the third LED 304 indicates that thisthird LED 304 is incorporated into the pulse oximeter when theratiometric method is used; it is unnecessary for the constantsaturation method. When the third LED 304 is used, the multiplexer 400acts as an analog switch between all three LED 300, 302, and 304signals. If the third LED 304 is utilized, feedback loops between themicroprocessor 420 and the first and second programmable gain amplifier374 and 394 in the λc wavelength path are also formed.

For pulse oximetry measurements using the ratiometric method, thesignals (logarithm converted) transmitted through the finger 310 at eachwavelength λa, λb, and λc are:

$\begin{matrix}\begin{matrix}{{S_{\lambda \; a}(t)} = {S_{\lambda \; {red}\; 1}(t)}} \\{= {{ɛ_{{{HbO}\; 2},{\lambda \; a}}c_{{HbO}\; 2}^{A}{x^{A}(t)}} + {ɛ_{{Hb},{\lambda \; a}}c_{Hb}^{A}{x^{A}(t)}} +}} \\{{{{ɛ_{{{HbO}\; 2},{\lambda \; a}}c_{{HbO}\; 2}^{V}{x^{V}(t)}} + {ɛ_{{Hb},{\lambda \; a}}c_{Hb}^{V}{x^{V}(t)}} + {n_{\lambda \; a}(t)}};}}\end{matrix} & (93) \\\begin{matrix}{{S_{\lambda \; b}(t)} = {S_{\lambda \; {red}\; 2}(t)}} \\{= {{ɛ_{{{HbO}\; 2},{\lambda \; b}}c_{{HbO}\; 2}^{A}{x^{A}(t)}} + {ɛ_{{Hb},{\lambda \; b}}c_{Hb}^{A}{x^{A}(t)}} +}} \\{{{{ɛ_{{{HbO}\; 2},{\lambda \; b}}c_{{HbO}\; 2}^{V}{x^{V}(t)}} + {ɛ_{{Hb},{\lambda \; b}}c_{Hb}^{V}{x^{V}(t)}} + {n_{\lambda \; b}(t)}};}}\end{matrix} & (94) \\\begin{matrix}{{S_{\lambda \; c}(t)} = {S_{\lambda \; {IR}}(t)}} \\{= {{ɛ_{{{HbO}\; 2},{\lambda \; c}}c_{{HbO}\; 2}^{A}{x^{A}(t)}} + {ɛ_{{Hb},{\lambda \; c}}c_{Hb}^{A}{x^{A}(t)}} +}} \\{{{ɛ_{{{HbO}\; 2},{\lambda \; c}}c_{{HbO}\; 2}^{V}{x^{V}(t)}} + {ɛ_{{Hb},{\lambda \; c}}c_{Hb}^{V}{x^{V}(t)}} + {{n_{\lambda \; c}(t)}.}}}\end{matrix} & (95)\end{matrix}$

In equations (93) through (95), x^(A)(t) is the lump-sum thickness ofthe arterial blood in the finger; x^(V)(t) is the lump-sum thickness ofvenous blood in the finger; ε_(HbO2,λa) ε_(HbO2,λb), ε_(HbO2,λc),ε_(Hb,λa), ε_(Hb,λb), and ε_(Hb,λc) are the absorption coefficients ofthe oxygenated and non-oxygenated hemoglobin, at each wavelengthmeasured; and c_(HbO2)(t) and c_(Hb)(t) with the superscriptdesignations A and V are the concentrations of the oxygenated andnon-oxygenated arterial blood and venous blood, respectively.

For the ratiometric method, the wavelengths chosen are typically two inthe visible red range, i.e. λa and λb, and one in the infrared range,i.e., λc. As described above, the measurement wavelengths λa and λb areadvantageously chosen to satisfy a proportionality relationship whichremoves the primary signal portions s_(λa)(t) and s_(λb)(t), yielding asecondary reference n′(t). In the preferred embodiment, the ratiometricmethod is used to determine the secondary reference signal n′(t) bypicking two wavelengths that cause the primary portions s_(λa)(t) ands_(λb)(t) of the measured signals S_(λa)(t) and S_(λb)(t) to becomelinearly dependent similarly to equation (22); i.e. wavelengths λa andλb which satisfy:

ε_(HbO2,λa)/ε_(Hb,λa)=ε_(HbO2,λb)/ε_(Hb,λb)  (96)

Typical wavelength values chosen are λa=650 nm and λb=685 nm.Additionally a typical wavelength value for λc is λc=940 nm. By pickingwavelengths λa and λb to satisfy equation (96) the venous portion of themeasured signal is also caused to become linearly dependent even thoughit is not usually considered to be part of the primary signals as is thecase in the constant saturation method. Thus, the venous portion of thesignal is removed with the primary portion of the constant saturationmethod. The proportionality relationship between equations (93) and (94)which allows determination of a non-zero secondary reference signaln′(t), similarly to equation (25) is:

ω_(av)=ε_(Hb,λa)/ε_(Hb,λb); where  (97)

n_(λa(t))=ω_(av)n_(λa(t)).  (98)

In pulse oximetry, both equations (97) and (98) can typically besatisfied simultaneously.

FIG. 12 is a graph of the absorption coefficients of oxygenated anddeoxygenated hemoglobin (ε_(HbO2) and ε_(Hb)) vs. wavelength (λ). FIG.13 is a graph of the ratio of the absorption coefficients vs.wavelength, i.e., ε_(Hb)/ε_(HbO2) vs. λ over the range of wavelengthwithin circle 13 in FIG. 12. Anywhere a horizontal line touches thecurve of FIG. 13 twice, as does line 400, the condition of equation (96)is satisfied. FIG. 14 shows an exploded view of the area of FIG. 12within the circle 13. Values of ε_(HbO2) and ε_(Hb) at the wavelengthswhere a horizontal line touches the curve of FIG. 13 twice can then bedetermined from the data in FIG. 14 to solve for the proportionalityrelationship of equation (97).

A special case of the ratiometric method is when the absorptioncoefficients ε_(HbO2) and ε_(Hb) are equal at a wavelength. Arrow 410 inFIG. 12 indicates one such location, called an isobestic point. FIG. 14shows an exploded view of the isobestic point. To use isobestic pointswith the ratiometric method, two wavelengths at isobestic points aredetermined to satisfy equation (96)

Multiplying equation (94) by ω_(a)v and then subtracting equation (94)from equation (93), a non-zero secondary reference signal n′(t) isdetermined by:

n′(t)=S _(λa)(t)−ω_(av) s _(λb)(t)=n _(λa)(t)−ω_(av) n _(λb)(t)  (99)

This secondary reference signal n′(t) has spectral content correspondingto the erratic, motion-induced noise. When it is input to a correlationcanceler, such as an adaptive noise canceler, with either the signalsS_(λa)(t) and S_(λc)(t) or S_(λb)(t) and S_(λc)(t) input to tworegression filters 80 a and 80 b as in FIG. 10, the adaptive noisecanceler will function much like an adaptive multiple notch filter andremove frequency components present in both the secondary referencesignal n′(t) and the measured signals from the measured signalsS_(λa)(t) and S_(λc)(t) or S_(λb)(t) and S_(λc)(t). If the secondaryreference signal n′(t) is correlated to the venous portion, then theadaptive noise canceler is able to remove erratic noise caused in thevenous portion of the measured signals S_(λa)(t), S_(λb)(t), andS_(λc)(t) even though the venous portion of the measured signalsS_(λa)(t) and S_(λb)(t) was not incorporated in the secondary referencesignal n′(t). In the event that the secondary reference signal n′(t) isnot correlated to the venous component, then, the adaptive noisecanceler generally will not remove the venous portion from the measuredsignals. However, a band pass filter applied to the approximations tothe primary signals s″_(λa)(t) and s″_(λc)(t) or s″_(λb)(t) ands″_(λc)(t) can remove the low frequency venous signal due to breathing.

For pulse oximetry measurements using the constant saturation method,the signals (logarithm converted) transmitted through the finger 310 ateach wavelength λa and λb are:

S _(λa)(t)=S _(λred1)(t)=ε_(HbO2,λa) c ^(A) _(HbO2) x ^(A)(t)+ε_(Hb,λa)c ^(A) _(Hb) x ^(A)(t)+ε_(HbO2,λa) c ^(V) _(HbO2) x ^(V)(t)+ε_(Hb,λa) c^(V) _(Hb) x ^(V)(t)+n _(λa)(t);  (100a)

S _(λa)(t)=ε_(HbO2,λa) c ^(A) _(HbO2) x ^(A)(t)+ε_(Hb,λa) c ^(A) _(Hb) x^(A)(t)+n _(λa)(t);  (100b)

S _(λa)(t)=s _(λa)(t)+n _(λa)(t);  (100c)

S _(λb)(t)=S _(λred2)(t)=ε_(HbO2,λb) c ^(A) _(HbO2) x ^(A)(t)+ε_(Hb,λb)c ^(A) _(Hb) x ^(A)(t)+ε_(HbO2,λb) c ^(V) _(HbO2) x ^(V)(t)+ε_(Hb,λb) c^(V) _(Hb) x ^(V)(t)+n _(λb)(t);  (101a)

S _(λb)(t)=ε_(HbO2,λb) c ^(A) _(HbO2) x ^(A)(t)+ε_(Hb,λb) c ^(A) _(Hb) x^(A)(t)+n _(λb)(t);  (101b)

S _(λb)(t)=S _(λb)(t)+n _(λb)(t).  (101c)

For the constant saturation method, the wavelengths chosen are typicallyone in the visible red range, i.e., λa, and one in the infrared range,i.e., λb. Typical wavelength values chosen are λa=660 nm and λb=940 nm.Using the constant saturation method, it is assumed that c^(A)_(HbO2)(t)/c^(A) _(Hb)(t)=constant₁ and c^(V) _(HbO2)(t)/c^(V)_(Hb)(t)=constant₂. The oxygen saturation of arterial and venous bloodchanges slowly, if at all, with respect to the sample rate, making thisa valid assumption. The proportionality factors for equations (100) and(101) can then be written as:

$\begin{matrix}{{\omega_{a}(t)} = {\frac{\in_{{{Hb}\; 02},{\lambda \; a}}{{c_{{Hb}\; 02}^{A}{x(t)}} +} \in_{{Hb},{\lambda \; a}}{c_{Hb}{x(t)}}}{\in_{{{Hb}\; 02},{\lambda \; b}}{{c_{{Hb}\; 02}^{A}{x(t)}} +} \in_{{Hb},{\lambda \; b}}{c_{Hb}{x(t)}}}*}} & (102) \\{{s_{\lambda \; a}(t)} = {{\omega_{a}(t)}{s_{\lambda \; b}(t)}}} & \left( {103a} \right) \\{{n_{\lambda \; a}(t)} \neq {{\omega_{a}(t)}{n_{\lambda \; b}(t)}}} & \left( {104a} \right) \\{{n_{\lambda \; a}(t)} = {{\omega_{v}(t)}{n_{\lambda \; b}(t)}}} & \left( {103b} \right) \\{{s_{\lambda \; a}(t)} \neq {{\omega_{v}(t)}{s_{\lambda \; b}(t)}}} & \left( {104b} \right)\end{matrix}$

In pulse oximetry, it is typically the case that both equations (103)and (104) can be satisfied simultaneously.

Multiplying equation (101) by ω_(a)(t) and then subtracting equation(101) from equation (100), a non-zero secondary reference signal n′(t)is determined by:

$\begin{matrix}\begin{matrix}{{n^{\prime}(t)} = {{S_{\lambda \; a}(t)} - {{\omega_{a}(t)}{S_{\lambda \; b}(t)}}}} \\{= {{ɛ_{{{HbO}\; 2},{\lambda \; a}}c_{{HbO}\; 2}^{V}{x^{V}(t)}} + {ɛ_{{Hb},{\lambda \; a}}c_{Hb}^{V}{x^{V}(t)}} + {n_{\lambda \; a}(t)} -}}\end{matrix} & \left( {105a} \right) \\{\mspace{79mu} {{\omega_{a}(t)}\left\lbrack {{ɛ_{{{HbO}\; 2},{\lambda \; b}}c_{{HbO}\; 2}^{V}{x^{V}(t)}} + {ɛ_{{Hb},{\lambda \; b}}c_{Hb}^{V}{x^{V}(t)}} + {n_{\lambda \; b}(t)}} \right\rbrack}} & \left( {106a} \right)\end{matrix}$

Multiplying equation (101) by ω_(v)(t) and then subtracting equation(101) from equation (100), a non-zero primary reference signal s′(t) isdetermined by:

$\begin{matrix}{{s^{\prime}(t)} = {{S_{\lambda \; a}(t)} - {{\omega_{v}(t)}{S_{\lambda \; b}(t)}}}} & \left( {105b} \right) \\{\mspace{45mu} {= {{s_{\lambda \; a}(t)} - {{\omega_{v}(t)}{s_{\lambda \; b}(t)}}}}} & \left( {106b} \right)\end{matrix}$

The constant saturation assumption does not cause the venouscontribution to the absorption to be canceled along with the primarysignal portions s_(λa)(t) and s_(λb)(t), as did the relationship ofequation (96) used in the ratiometric method. Thus, frequenciesassociated with both the low frequency modulated absorption due tovenous absorption when the patient is still and the erraticallymodulated absorption due to venous absorption when the patient is movingare represented in the secondary reference signal n′(t). Thus, thecorrelation canceler can remove or derive both erratically modulatedabsorption due to venous blood in the finger under motion and theconstant low frequency cyclic absorption of venous blood.

Using either method, a primary reference s′(t) or a secondary referencen′(t) is determined by the processor of the present invention for use ina correlation canceler, such as an adaptive noise canceler, which isdefined by software in the microprocessor. The preferred adaptive noisecanceler is the joint process estimator 60 described above.

Illustrating the operation of the ratiometric method of the presentinvention, FIGS. 15, 16 and 17 show signals measured for use indetermining the saturation of oxygenated arterial blood using areference processor of the present invention which employs theratiometric method, i.e., the signals S_(λa)(t)=S_(λred1)(t), S_(λb)(t)S_(λred2)(t), and S_(λc)(t)=S_(λIR)(t). A first segment 15 a, 16 a, and17 a of each of the signals is relatively undisturbed by motionartifact, i.e., the patient did not move substantially during the timeperiod in which these segments were measured. These segments 15 a, 16 a,and 17 a are thus generally representative of the plethysmographicwaveform at each of the measured wavelengths. These waveforms are takento be the primary signals s_(λa)(t), s_(λb)(t), and s_(λc)(t). A secondsegment 15 b, 16 b, and 17 b of each of the signals is affected bymotion artifact, i.e., the patient did move during the time period inwhich these segments were measured. Each of these segments 15 b, 16 b,and 17 b shows large motion induced excursions in the measured signal.These waveforms contain both primary plethysmographic signals andsecondary motion induced excursions. A third segment 15 c, 16 c, and 17c of each of the signals is again relatively unaffected by motionartifact and is thus generally representative of the plethysmographicwaveform at each of the measured wavelengths.

FIG. 18 shows the secondary reference signal n′(t)=n_(λa)−ω_(a)vn_(λa)(t), as determined by a reference processor of the presentinvention utilizing the ratiometric method. As discussed previously, thesecondary reference signal n′(t) is correlated to the secondary signalportions n_(λa), n_(λb), and n _(λc). Thus, a first segment 18 a of thesecondary reference signal n′(t) is generally flat, corresponding to thefact that there is very little motion induced noise in the firstsegments 15 a, 16 a, and 17 a of each signal. A second segment 18 b ofthe secondary reference signal n′(t) exhibits large excursions,corresponding to the large motion induced excursions in each of themeasured signals. A third segment 18 c of the secondary reference signaln′(t) is generally flat, again corresponding to the lack of motionartifact in the third segments 15 c, 16 c, and 17 c of each measuredsignal.

FIG. 19 shows the primary reference signal s′(t)=s_(λa)−ω_(e)s_(λb)(t),as determined by a reference processor of the present inventionutilizing the ratiometric method. As discussed previously, the primaryreference signal s′(t) is correlated to the primary signal portionss_(λa)(t), s_(λb)(t), and s_(λc)(t). Thus, a first segment 19 a of theprimary reference signal s′(t) is indicative of the plethysmographicwaveform, corresponding to the fact that there is very little motioninduced noise in the first segments 15 a, 16 a, and 17 a of each signal.A second segment 19 b of the primary reference signal s′(t) alsoexhibits a signal related to a plethymographic waveform, correspondingto each of the measured signals in the absence of the large motioninduced excursions. A third segment 19 c of the primary reference signals′(t) is generally indicative of the plethysmographic waveform, againcorresponding to the lack of motion artifact in the third segments 15 c,16 c, and 17 c of each measured signal.

FIGS. 20 and 21 show the approximations s″_(λa)(t) and s″_(λc)(t) to theprimary signals s_(λa)(t) and s_(λc)(t) as estimated by the correlationcanceler 27 using a secondary reference signal n′(t) determined by theratiometric method. FIGS. 20 and 21 illustrate the effect of correlationcancelation using the secondary reference signal n′(t) as determined bythe reference processor of the present invention using the ratiometricmethod. Segments 20 b and 21 b are not dominated by motion induced noiseas were segments 15 b, 16 b, and 17 b of the measured signals.Additionally, segments 20 a, 21 a, 20 c, and 21 c have not beensubstantially changed from the measured signal segments 15 a, 17 a, 15c, and 17 c where there was no motion induced noise.

FIGS. 22 and 23 show the approximations n″_(λa)(t) and n″_(λc)(t) to theprimary signals n_(λa)(t) and n_(λc)(t) as estimated by the correlationcanceler 27 using a primary reference signal s′(t) determined by theratiometric method. Note that the scale of FIGS. 15 through 23 is notthe same for each figure to better illustrate changes in each signal.FIGS. 22 and 23 illustrate the effect of correlation cancelation usingthe primary reference signal s′(t) as determined by the referenceprocessor of the present invention using the ratiometric method. Onlysegments 22 b and 23 b are dominated by motion induced noise as weresegments 15 b, 16 b, and 17 b of the measured signals. Additionally,segments 22 a, 23 a, 22 c, and 23 c are nearly zero corresponding to themeasured signal segments 15 a, 17 a, 15 c, and 17 c where there was nomotion induced noise.

Illustrating the operation of the constant saturation method of thepresent invention, FIGS. 24 and 25 show signals measured for input to areference processor of the present invention which employs the constantsaturation method, i.e., the signals S_(λa)(t)=S_(λred)(t) andSλb(t)=S_(λIR)(t). A first segment 24 a and 25 a of each of the signalsis relatively undisturbed by motion artifact, i.e., the patient did notmove substantially during the time period in which these segments weremeasured. These segments 24 a and 25 a are thus generally representativeof the primary plethysmographic waveform at each of the measuredwavelengths. A second segment 24 b and 25 b of each of the signals isaffected by motion artifact, i.e., the patient did move during the timeperiod in which these segments were measured. Each of these segments 24b and 25 b shows large motion induced excursions in the measured signal.A third segment 24 c and 25 c of each of the signals is again relativelyunaffected by motion artifact and is thus generally representative ofthe primary plethysmographic waveform at each of the measuredwavelengths.

FIG. 26 shows the secondary reference signaln′(t)=n_(λa)(t)−ω_(a)n_(λa)(t), as determined by a reference processorof the present invention utilizing the constant saturation method.Again, the secondary reference signal n′(t) is correlated to thesecondary signal portions n_(λa) and n_(λb). Thus, a first segment 26 aof the secondary reference signal n′(t) is generally flat, correspondingto the fact that there is very little motion induced noise in the firstsegments 24 a and 25 a of each signal. A second segment 26 b of thesecondary reference signal n′(t) exhibits large excursions,corresponding to the large motion induced excursions in each of themeasured signals. A third segment 26 c of the noise reference signaln′(t) is generally flat, again corresponding to the lack of motionartifact in the third segments 24 c and 25 c of each measured signal.

FIG. 27 shows the primary reference signal s′(t)=s_(λa)−ω_(v)s_(λb)(t),as determined by a reference processor of the present inventionutilizing the constant saturation method. As discussed previously, theprimary reference signal s′(t) is correlated to the primary signalportions s_(λa)(t) and s_(λb)(t). Thus, a first segment 27 a of theprimary reference signal s′(t) is indicative of the plethysmographicwaveform, corresponding to the fact that there is very little motioninduced noise in the first segments 24 a and 25 a of each signal. Asecond segment 27 b of the primary reference signal s′(t) also exhibitsa signal related to a plethymographic waveform, corresponding to each ofthe measured signals in the absence of the large motion inducedexcursions. A third segment 27 c of the primary reference signal s′(t)is generally indicative of the plethysmographic waveform, againcorresponding to the lack of motion artifact in the third segments 24 cand 25 c of each measured signal.

FIGS. 28 and 29 show the approximations s″_(λa)(t) and s″_(λb)(t) to theprimary signals s_(λa)(t) and s_(λb)(t) as estimated by the correlationcanceler 27 using a secondary reference signal n′(t) determined by theconstant saturation method. FIGS. 28 and 29 illustrate the effect ofcorrelation cancelation using the secondary reference signal n′(t) asdetermined by a reference processor of the present invention utilizingthe constant saturation method. Segments 28 b and 28 b are not dominatedby motion induced noise as were segments 24 b and 25 b of the measuredsignals. Additionally, segments 28 a, 29 a, 28 c, and 29 c have not beensubstantially changed from the measured signal segments 24 a, 25 a, 24c, and 25 c where there was no motion induced noise.

FIGS. 30 and 31 show the approximations n″_(λa)(t) and n″_(λb)(t) to thesecondary signals n_(λa)(t) and n_(λb)(t) as estimated by thecorrelation canceler 27 using a primary reference signal s′(t)determined by the constant saturation method. Note that the scale ofFIGS. 24 through 31 is not the same for each figure to better illustratechanges in each signal. FIGS. 30 and 31 illustrate the effect ofcorrelation cancelation using the primary reference signal s′(t) asdetermined by a reference processor of the present invention utilizingthe constant saturation method. Only segments 30 b and 31 b aredominated by motion induced noise as were segments 24 b, and 25 b of themeasured signals. Additionally, segments 30 a, 31 a, 30 c, and 31 c arenearly zero corresponding to the measured signal segments 24 a, 25 a, 24c, and 25 c where there was no motion induced noise.

Method for Estimating Primary and Secondary Signal Portion of MeasuredSignals in a Pulse Oximeter

A copy of a computer subroutine, written in the C programming language,calculates a primary reference s′(t) and a secondary reference n′(t)using the ratiometric method and, using a joint process estimator 60,estimates either the primary or secondary signal portions of twomeasured signals, each having a primary signal which is correlated withthe primary reference s′(t) and having a secondary signal which iscorrelated with the secondary reference n′(t), is appended in AppendixA. For example, S_(λa)(t)=S_(λred)(t)=S_(λ660nm)(t) andS_(λb)(t)=S_(λIR)(t)=S_(λ940nm)(t) can be input to the computersubroutine. This subroutine is one way to implement the stepsillustrated in the flowchart of FIG. 9 for a monitor particularlyadapted for pulse oximetry.

The program estimates either the primary signal portions or thesecondary signal portions of two light energy signals, one preferablycorresponding to light in the visible red range and the other preferablycorresponding to light in the infrared range such that a determinationof the amount of oxygen, or the saturation of oxygen in the arterial andvenous blood components, may be made. The calculation of the saturationis performed in a separate subroutine.

Using the ratiometric method three signals S_(λa)(t), S_(λb)(t) andS_(λc)(t) are input to the subroutine. S_(λa)(t) and S_(λb)(t) are usedto calculate either the primary or secondary reference signal s′(t) orn′(t). As described above, the wavelengths of light at which S_(λa)(t)and S_(λb)(t) are measured are chosen to satisfy the relationship ofequation (96). Once either the secondary reference signal n′(t) or theprimary reference signal s′(t) is determined, either the primary signalportions s_(λa)(t) and s_(λc)(t) or the secondary signal portionsn_(λa)(t) and n_(λc)(t) of the measured signals S_(λa)(t) and S_(λc)(t)are estimated for use in calculation of the oxygen saturation.

The correspondence of the program variables to the variables defined inthe discussion of the joint process estimator is as follows:

-   -   Δ_(m)(t)=nc[m].Delta    -   Γ_(f,m)(t)=nc[m].fref    -   Γ_(b,m)(t)=nc[m].bref    -   f_(m)(t)=nc[m].ferr    -   b_(m)(t)=nc[m].berr    -   J_(m)(t)=nc[m].Fswsqr    -   β_(m)(t)=nc[m].Bswsqr    -   γ_(m)(t)=nc[m].Gamma    -   ρ_(m,λa)(t)=nc[m].Roh_a    -   ρ_(m,λc)(t)=nc[m].Roh_c    -   e_(m,λa)(t)=nc[m].err_a    -   e_(m,λc)(t)=nc[m].err_c    -   κ_(m,λa)(t)=nc[m].K_a    -   κ_(m,λc)(t)=nc[m].K_c

A first portion of the program performs the initialization of theregisters 90, 92, 96, and 98 and intermediate variable values as in the“INITIALIZE CORRELATION CANCELER” box 120 and equations (52) through(56) and equations (73), (74), (77), and (78). A second portion of theprogram performs the time updates of the delay element variables 110where the value at the input of each delay element variable 110 isstored in the delay element variable 110 as in the “TIME UPDATE OF [Z⁻¹]ELEMENTS” box 130.

A third portion of the program calculates the reference signal, as inthe “CALCULATE SECONDARY REFERENCE (n′(t)) OR PRIMARY REFERENCE (s′(t))FOR TWO MEASURED SIGNAL SAMPLES” box 140 using the proportionalityconstant ω_(a)v determined by the ratiometric method as in equation(25).

A fourth portion of the program performs the zero-stage update as in the“ZERO-STAGE UPDATE” box 150 where the zero-stage forward predictionerror f₀(t) and the zero-stage backward prediction error b₀(t) are setequal to the value of the reference signal n′(t) or s′(t) justcalculated. Additionally, zero-stage values of intermediate variablesJ₀(t) and β₀(t) (nc[m].Fswsqr and nc[m].Bswsqr in the program) arecalculated for use in setting register 90, 92, 96, and 98 values in theleast-squares lattice predictor 70 and the regression filters 80 a and80 b.

A fifth portion of the program is an iterative loop wherein the loopcounter, m, is reset to zero with a maximum of m=NC_CELLS, as in the“m=0” box 160 in FIG. 9. NC_CELLS is a predetermined maximum value ofiterations for the loop. A typical value of NC_CELLS is between 6 and10, for example. The conditions of the loop are set such that the loopiterates a minimum of five times and continues to iterate until a testfor conversion is met or m=NC_CELLS. The test for conversion is whetheror not the sum of the weighted sum of forward prediction errors plus theweighted sum of backward prediction errors is less than a small number,typically 0.00001 (i.e, J_(m)(t)+β_(m)(t)≦0.00001).

A sixth portion of the program calculates the forward and backwardreflection coefficient Γ_(m,f)(t) and Γ_(m,b)(t) register 90 and 92values (nc[m].fref and nc[m].bref in the program) as in the “ORDERUPDATE m^(th)-STAGE OF LSL-PREDICTOR” box 170 and equations (61) and(62). Then forward and backward prediction errors f_(m)(t) and b_(m)(t)(nc[m].ferr and nc[m].berr in the program) are calculated as inequations (63) and (64). Additionally, intermediate variables J_(m)(t),β_(m)(t) and γ_(m)(t) (nc[m].Fswsqr, nc[m].Bswsqr, nc[m].Gamma in theprogram) are calculated, as in equations (65), (66), and (67). The firstcycle of the loop uses the values for nc[0].Fswsqr and nc[0].Bswsqrcalculated in the ZERO-STAGE UPDATE portion of the program.

A seventh portion of the program, still within the loop, calculates theregression coefficient κ_(m,λa)(t) and κ_(m,λc)(t) register 96 and 98values (nc[m].K_a and nc[m].K_c in the program) in both regressionfilters, as in the “ORDER UPDATE m^(th) STAGE OF REGRESSION FILTER(S)”box 180 and equations (68) through (80). Intermediate error signals andvariables e_(m,λa)(t), e_(m,λc)(t), ρ.m_(,λa)(t), and ρ_(m,λc)(t)(nc[m].err_a and nc[m].err_c, nc[m].roh_a, and nc[m].roh_c in thesubroutine) are also calculated as in equations (75), (76), (71), and(72), respectively.

The test for convergence of the joint process estimator is performedeach time the loop iterates, analogously to the “DONE” box 190. If thesum of the weighted sums of the forward and backward prediction errorsJ_(m)(t)+β_(m)(t) is less than or equal to 0.00001, the loop terminates.Otherwise, the sixth and seventh portions of the program repeat.

When either the convergence test is passed or m=NC_CELLS, an eighthportion of the program calculates the output of the joint processestimator 60 as in the “CALCULATE OUTPUT” box 200. This output is a goodapproximation to both of the primary signals s″_(λa)(t) and s″_(λc)(t)or the secondary signals n″_(λa)(t) and n″_(λc)(t) for the set ofsamples S_(λa)(t) and S_(λc)(t), input to the program. After many setsof samples are processed by the joint process estimator, a compilationof the outputs provides output waves which are good approximations tothe plethysmographic wave or motion artifact at each wavelength, λa andλc.

Another copy of a computer program subroutine, written in the Cprogramming language, which calculates either a primary reference s′(t)or a secondary reference n′(t) using the constant saturation method and,using a joint process estimator 60, estimates a good approximation toeither the primary signal portions or secondary signal portions of twomeasured signals, each having a primary portion which is correlated tothe primary reference signal s′(t) and a secondary portion which iscorrelated to the secondary reference signal n′(t) and each having beenused to calculate the reference signals s′(t) and n′(t), is appended inAppendix B. This subroutine is another way to implement the stepsillustrated in the flowchart of FIG. 9 for a monitor particularlyadapted for pulse oximetry. The two signals are measured at twodifferent wavelengths λa and λb, where λa is typically in the visibleregion and λb is typically in the infrared region. For example, in oneembodiment of the present invention, tailored specifically to performpulse oximetry using the constant saturation method, λa=660 nm andλb=940 nm.

The correspondence of the program variables to the variables defined inthe discussion of the joint process estimator is as follows:

-   -   Δ_(m)(t)=nc[m].Delta    -   Γ_(f,m)(t)=nc[m].fref    -   Γ_(b,m)(t)=nc[m].bref    -   f_(m)(t)=nc[m].ferr    -   b_(m)(t)=nc[m].berr    -   ℑ_(m)(t)=nc[m].Fswsqr    -   β_(m)(t)=nc[m].Bswsqr    -   γ_(m)(t)=nc[m].Gamma    -   ρ_(m,λa)(t)=nc[m].Roh_a    -   ρ_(m,λb)(t)=nc[m].Roh_b    -   e_(m,λa)(t)=nc[m].err_a    -   e_(m,λb)(t)=nc[m].err_b    -   κ_(m,λa)(t)=nc[m].K_a    -   κ_(m,λb)(t)=nc[m].K_b

First and second portions of the subroutine are the same as the firstand second portions of the above described subroutine tailored for theratiometric method of determining either the primary reference s′(t) orthe noise reference n′(t). The calculation of saturation is performed ina separate module. Various methods for calculation of the oxygensaturation are known to those skilled in the art. One such calculationis described in the articles by G. A. Mook, et al, and Michael R. Neumancited above. Once the concentration of oxygenated hemoglobin anddeoxygenated hemoglobin are determined, the value of the saturation isdetermined similarly to equations (85) through (92) wherein measurementsat times t₁ and t₂ are made at different, yet proximate times over whichthe saturation is relatively constant. For pulse oximetry, the averagesaturation at time t=(t₁+t₂)/2 is then determined by:

$\begin{matrix}{{{Saturation}_{Art}(t)} = \frac{C_{{Hb}\; 02}^{A}(t)}{{C_{{Hb}\; 02}^{A}(t)} + {C_{Hb}^{A}(t)}}} & (107) \\{\mspace{169mu} {= \frac{\in_{{Hb},{\lambda \; a}}{- {\in_{{Hb},{\lambda \; b}}\left( {\Delta \; {S_{\lambda \; a}/\Delta}\; S_{\lambda \; b}} \right)}}}{\begin{matrix}{\in_{{HB},{\lambda \; a}}{- {\in_{{{Hb}\; 02},{\lambda \; a}} -}}} \\{\left( {\in_{{HB},{\lambda \; b}}{- \in_{{{Hb}\; 02},{\lambda \; b}}}} \right)\left( {\Delta \; {S_{\lambda \; a}/\Delta}\; S_{\lambda \; b}} \right)}\end{matrix}}}} & \left( {107b} \right) \\{{{Saturation}_{Ven}(t)} = \frac{C_{{Hb}\; 02}^{V}(t)}{{C_{{Hb}\; 02}^{V}(t)} + {C_{Hb}^{V}(t)}}} & \left( {108a} \right) \\{\mspace{169mu} {= \frac{\in_{{Hb},{\lambda \; a}}{- {\in_{{Hb},{\lambda \; b}}\left( {\Delta \; {n_{\lambda \; a}/\Delta}\; n_{\lambda \; b}} \right)}}}{\begin{matrix}{\in_{{HB},{\lambda \; a}}{- {\in_{{{Hb}\; 02},{\lambda \; a}} -}}} \\{\left( {\in_{{HB},{\lambda \; b}}{- \in_{{{Hb}\; 02},{\lambda \; b}}}} \right)\left( {\Delta \; {n_{\lambda \; a}/\Delta}\; n_{\lambda \; b}} \right)}\end{matrix}}}} & \left( {108b} \right)\end{matrix}$

A third portions of the subroutine calculates either the primaryreference or secondary reference, as in the “CALCULATE PRIMARY ORSECONDARY REFERENCE (s′(t) or n′(t)) FOR TWO MEASURED SIGNAL SAMPLES”box 140 for the signals S_(λa)(t) and S_(λb)(t) using theproportionality constants ω_(a)(t) and ω_(v)(t) determined by theconstant saturation method as in equation (3). The saturation iscalculated in a separate subroutine and a value of ω_(a)(t) or ω_(v)(t)is imported to the present subroutine for estimating either the primaryportions s_(λa)(t) and s_(λb)(t) or the secondary portions n_(λa)(t) andn_(λb)(t) of the composite measured signals S_(λa)(t) and S_(λb)(t).

Fourth, fifth, and sixth portions of the subroutine are similar to thefourth, fifth, and sixth portions of the above described programtailored for the ratiometric method. However, the signals being used toestimate the primary signal portions s_(λa)(t) and s_(λb)(t) or thesecondary signal portions n_(λa)(t) and n_(λb)(t) in the presentsubroutine tailored for the constant saturation method, are S_(λa)(t)and S_(λb)(t), the same signals that were used to calculate thereference signal s′(t) or n′(t).

A seventh portion of the program, still within the loop begun in thefifth portion of the program, calculates the regression coefficientregister 96 and 98 values κ_(m,λa)(t) and κ_(m,λb)(t) (nc[m].K_a andnc[m].K_b in the program) in both regression filters, as in the “ORDERUPDATE m^(th) STAGE OF REGRESSION FILTER(S)” box 180 and equations (68)through (80). Intermediate error signals and variables e_(m,λa)(t),e_(m,λb)(t), ρ_(m,λa)(t), and ρ_(m,λb)(t) (nc[m].err_a and nc[m].err_b,nc[m].roh_a, and nc[m].roh_b in the subroutine) are also calculated asin equations (70), (75), (68), and (71), respectively.

The loop iterates until the test for convergence is passed, the testbeing the same as described above for the subroutine tailored for theratiometric method. The output of the present subroutine is a goodapproximation to the primary signals s″_(λa)(t) and s″_(λb)(t) or thesecondary signals n″_(λa)(t) and n″_(λb)(t) for the set of samplesS_(λa)(t) and S_(λb)(t) input to the program. After approximations tothe primary signal portions or the secondary signals portions of manysets of measured signal samples are estimated by the joint processestimator, a compilation of the outputs provides waves which are goodapproximations to the plethysmographic wave or motion artifact at eachwavelength, λa and λb. The estimating process of the iterative loop isthe same in either subroutine, only the sample values S_(λa)(t) andS_(λc)(t) or S_(λa)(t) and S_(λb)(t) input to the subroutine for use inestimation of the primary signal portions s_(λa)(t) and s_(λc)(t) ors_(λa)(t) and s_(λb)(t) or of the secondary signal portions n_(λa)(t)and n_(λc)(t) or n_(λa)(t) and n_(λb)(t) and how the primary andsecondary reference signals s′(t) and n′(t) are calculated are differentfor the ratiometric method and the constant saturation methods.

Independent of the method used, ratiometric or constant saturation, theapproximations to either the primary signal values or the secondarysignal values are input to a separate subroutine in which the saturationof oxygen in the arterial and venous blood is calculated. If theconstant saturation method is used, the saturation calculationsubroutine also determines values for the proportionality constantsωa(t) and ω_(v)(t) as defined in equation (3) and discussed above. Theconcentration of oxygenated arterial and venous blood can be found fromthe approximations to the primary or secondary signal values since theyare made up of terms comprising x(t), the thickness of arterial andvenous blood in the finger; absorption coefficients of oxygenated andde-oxygenated hemoglobin, at each measured wavelength; and c_(HbO2)(t)and c_(Hb)(t), the concentrations of oxygenated and de-oxygenatedhemoglobin, respectively. The saturation is a ratio of the concentrationof one constituent, A₅, with respect to the total concentration ofconstituents in the volume containing A₅ and A₆ or the ratio of theconcentration of one constituent A₃, with respect to the totalconcentration of constituents in the volume containing A₃ and A₄. Thus,the thickness, x(t), is divided out of the saturation calculation andneed not be predetermined. Additionally, the absorption coefficients areconstant at each wavelength. The saturation of oxygenated arterial andvenous blood is then determined as in equations (107) and (108).

While one embodiment of a physiological monitor incorporating aprocessor of the present invention for determining a reference signalfor use in a correlation canceler, such as an adaptive noise canceler,to remove or derive primary and secondary components from aphysiological measurement has been described in the form of a pulseoximeter, it will be obvious to one skilled in the art that other typesof physiological monitors may also employ the above describedtechniques.

Furthermore, the signal processing techniques described in the presentinvention may be used to compute the arterial and venous blood oxygensaturations of a physiological system on a continuous or nearlycontinuous time basis. These calculations may be performed, regardlessof whether or not the physiological system undergoes voluntary motion.The arterial pulsation induced primary plethysmographic signalss_(λa)(t) and s_(λb)(t) may be used to compute arterial blood oxygensaturation. The primary signals s_(λa)(t) and s_(λb)(t) can always beintroduced into the measured signals S_(λa)(t) and S_(λb)(t) if at leasttwo requirements are met. The two requirements include the selection oftwo or more flesh penetrating and blood absorbing wavelengths which areoptically modulated by the arterial pulsation and an instrument designwhich passes all or portions of all electromagnetic signals which arerelated to the pulsation. Similarly, the secondary signals n_(λa)(t) andn_(λb)(t) related to venous blood flow may be used to compute itscorresponding oxygen saturation. The secondary signal componentsn_(λa)(t) and n_(λb)(t) can be guaranteed to be contained in themeasured signals S_(λa)(t) and S_(λb)(t) if the two or more fleshpenetrating and blood absorbing wavelengths are processed to pass all orportions of all electromagnetic signals relating to venous blood flow.This may include but is not limited to all or portions of all signalswhich are related to the involuntary action of breathing. Similarly, itmust be understood that there are many different types of physicalsystems which may be configured to yield two or more measurement signalseach possessing a primary and secondary signal portion. In a great manyof such physical systems it will be possible to derive one or morereference signals. The reference signals may be used in conjunction witha correlation canceler, such as an adaptive noise canceler, to deriveeither the primary and/or secondary signal components of the two or moremeasurement signals on a continuous or intermittent time basis.

Another embodiment of a physiological monitor incorporating a processorof the present invention for determining a reference signal for use in acorrelation canceler, such as an adaptive noise canceler, to remove orderive primary and secondary components from a physiological measurementmay be described in the form of a instrument which measures bloodpressure. There are several ways of obtaining blood pressuremeasurements, such as tonometry, and pulse wave velocity. Both of thesemethods are substantially related to plethysmography.

Tonometry is a measurement method in which a direct reading of thearterial pressure pulse is made non-invasively. These measurements areinvariably made through the use of a piezoelectric force transducer, thesurface of which is gently pressed against a near-surface arterysupported by underlying bone. If the transducer is sufficiently pressedagainst the artery that its surface is in complete contact with thetissue; then, knowing its surface area, its output can be directly readas pressure. This “flattening” of the arterial wall leads to the name ofthis method, applanation tonometry. The pulse wave velocity techniquerelies on the concept that the speed with which the pressure pulse,generated at the heart, travels “down” the arterial system is dependenton pressure. In each of these cases plethysmographic waveforms are usedto determine the blood pressure of a patient.

Furthermore, it will be understood that transformations of measuredsignals other than logarithmic conversion and determination of aproportionality factor which allows removal or derivation of the primaryor secondary signal portions for determination of a reference signal arepossible. Additionally, although the proportionality factor ω has beendescribed herein as a ratio of a portion of a first signal to a portionof a second signal, a similar proportionality constant determined as aratio of a portion of a second signal to a portion of a first signalcould equally well be utilized in the processor of the presentinvention. In the latter case, a secondary reference signal wouldgenerally resemble n′(t)=n_(λb)(t)−ωn_(λa)(t).

Furthermore, it will be understood that correlation cancellationtechniques other than joint process estimation may be used together withthe reference signals of the present invention. These may include butare not limited to least mean square algorithms, wavelet transforms,spectral estimation techniques, neural networks, Weiner filters, Kalmanfilters, QR-decomposition based algorithms among others. Theimplementation that we feel is the best, as of this filing, is thenormalized least square lattice algorithm an implementation of which islisted in Appendix C.

It will also be obvious to one skilled in the art that for mostphysiological measurements, two wavelengths may be determined which willenable a signal to be measured which is indicative of a quantity of acomponent about which information is desired. Information about aconstituent of any energy absorbing physiological material may bedetermined by a physiological monitor incorporating a signal processorof the present invention and an correlation canceler by determiningwavelengths which are absorbed primarily by the constituent of interest.For most physiological measurements, this is a simple determination.

Moreover, one skilled in the art will realize that any portion of apatient or a material derived from a patient may be used to takemeasurements for a physiological monitor incorporating a processor ofthe present invention and a correlation canceler. Such areas include adigit such as a finger, but are not limited to a finger.

One skilled in the art will realize that many different types ofphysiological monitors may employ a signal processor of the presentinvention in conjunction with a correlation canceler, such as anadaptive noise canceler. Other types of physiological monitors include,but are in not limited to, electron cardiographs, blood pressuremonitors, blood gas saturation (other than oxygen saturation) monitors,capnographs, heart rate monitors, respiration monitors, or depth ofanesthesia monitors. Additionally, monitors which measure the pressureand quantity of a substance within the body such as a breathalizer, adrug monitor, a cholesterol monitor, a glucose monitor, a carbon dioxidemonitor, a glucose monitor, or a carbon monoxide monitor may also employthe above described techniques for removal of primary or secondarysignal portions.

Furthermore, one skilled in the art will realize that the abovedescribed techniques of primary or secondary signal removal orderivation from a composite signal including both primary and secondarycomponents can also be performed on electrocardiography (ECG) signalswhich are derived from positions on the body which are close and highlycorrelated to each other. It must be understood that a tripolarLaplacian electrode sensor such as that depicted in FIG. 32 which is amodification of a bipolar Laplacian electrode sensor discussed in thearticle “Body Surface Laplacian ECG Mapping” by Bin He and Richard J.Cohen contained in the journal IEEE Transactions on BiomedicalEngineering, Vol. 39, No. 11, November 1992 could be used as an ECGsensor. This article is hereby incorporated as reference. It must alsobe understood that there are a myriad of possible ECG sensor geometry'sthat may be used to satisfy the requirements of the present invention.

Furthermore, one skilled in the art will realize that the abovedescribed techniques of primary or secondary signal removal orderivation from a composite signal including both primary and secondarycomponents can also be performed on signals made up of reflected energy,rather than transmitted energy. One skilled in the art will also realizethat a primary or secondary portion of a measured signal of any type ofenergy, including but not limited to sound energy, X-ray energy, gammaray energy, or light energy can be estimated by the techniques describedabove. Thus, one skilled in the art will realize that the processor ofthe present invention and a correlation canceler can be applied in suchmonitors as those using ultrasound where a signal is transmitted througha portion of the body and reflected back from within the body backthrough this portion of the body. Additionally, monitors such as echocardiographs may also utilize the techniques of the present inventionsince they too rely on transmission and reflection.

While the present invention has been described in terms of aphysiological monitor, one skilled in the art will realize that thesignal processing techniques of the present invention can be applied inmany areas, including but not limited to the processing of aphysiological signal. The present invention may be applied in anysituation where a signal processor comprising a detector receives afirst signal which includes a first primary signal portion and a firstsecondary signal portion and a second signal which includes a secondprimary signal portion and a second secondary signal portion. The firstand second signals propagate through a common medium and the first andsecond primary signal portions are correlated with one another.Additionally, at least a portion of the first and second secondarysignal portions are correlated with one another due to a perturbation ofthe medium while the first and second signals are propagating throughthe medium. The processor receives the first and second signals and maycombine the first and second signals to generate a secondary referencein which is uncorrelated with the primary signal portions of themeasured signals or a primary reference which is uncorrelated with thesecondary signal portions of the measured signals. Thus, the signalprocessor of the present invention is readily applicable to numeroussignal processing areas.

1. A method determining a value of blood oxygen saturation of pulsingblood, the method comprising: receiving three or more intensity signalsfrom at least one light-sensitive detector which detects lightattenuated by body tissue carrying pulsing blood, wherein the three ormore intensity signals correspond to detection of at least threewavelengths of the light; and determining a value of oxygen saturationusing the three or more intensity signals, wherein the three or moreintensity signals include motion induced noise.
 2. The method of claim1, wherein the step of determining further comprises processing at leasttwo of the three or more intensity signals with an adaptive algorithm.3. The method of claim 2, wherein the adaptive algorithm comprises aleast squares algorithm.
 4. The method of claim 3, wherein the leastsquares algorithm comprises a least squares lattice.
 5. The method ofclaim 1, wherein the step of determining further comprises processing atleast two of the three or more intensity signals with a least squaresalgorithm.
 6. The method of claim 1, wherein one of the three or moreintensity signals corresponds to one of the at least three wavelengthsand is used primarily to reduce an effect of the motion induced noise onthe value of oxygen saturation.
 7. The method of claim 6, wherein two ofthe three or more intensity signals correspond to two of the at leastthree wavelengths and are used primarily to determine the value ofoxygen saturation.
 8. The method of claim 1, wherein absorptioncoefficients associated with two of the at least three wavelengths arerelated to one another.
 9. The method of claim 8, wherein absorptioncoefficients associated with two of the at least three wavelengths areproportional to one another.
 10. The method of claim 8, whereinabsorption coefficients associated with two of the at least threewavelengths are linearly proportional to one another.
 11. The method ofclaim 1, wherein absorption coefficients associated with the at leastthree wavelengths are proportional to one another.
 12. The method ofclaim 1, wherein each of the three or more intensity signals includes asignal portion and a noise portion, and wherein a non-zero referencesignal corresponds to the noise portion of one of the three or moreintensity signals.
 13. The method of claim 1, wherein each of the threeor more intensity signals includes a signal portion and a noise portion,and wherein a non-zero reference signal corresponds to the signalportion of one of the three or more intensity signals.
 14. The method ofclaim 1, wherein the pulsing blood comprises arterial blood.
 15. Themethod of claim 1, wherein the pulsing blood comprises venous blood. 16.A method of reducing an effect of motion induced noise on a plurality ofintensity signals during the determination of a parameter of pulsingblood, the method comprising: receiving a plurality of intensity signalsfrom at least one light-sensitive detector which detects light of aplurality of wavelengths attenuated by body tissue carrying pulsingblood; and processing one of the plurality of intensity signals usingdata from an additional intensity signal other than the plurality ofintensity signals, the additional intensity signal corresponding to anadditional wavelength of light, wherein the processing determines avalue of blood oxygen saturation of the pulsing blood during motioninduced noise, wherein the data from the extra wavelength is used toreduce an effect of the motion induced noise.
 17. The method of claim16, wherein the step of processing further comprises processing theplurality of intensity signals with an adaptive algorithm.
 18. Themethod of claim 17, wherein the adaptive algorithm comprises a leastsquares algorithm.
 19. The method of claim 18, wherein the least squaresalgorithm comprises a least squares lattice.
 20. The method of claim 16,wherein absorption coefficients associated with the plurality ofintensity signals are related to one another.
 21. The method of claim20, wherein absorption coefficients associated with the plurality ofintensity signals are proportional to one another.
 22. The method ofclaim 20, wherein absorption coefficients associated with the pluralityof intensity signals are linearly proportional to one another.
 23. Themethod of claim 16, wherein absorption coefficients associated with theplurality of intensity signals and the additional intensity signal areproportional to one another.
 24. The method of claim 16, wherein theplurality of intensity signals and the additional intensity signal eachincludes a signal portion and a noise portion, and wherein a non-zeroreference signal corresponds to the noise portion of one of theintensity signals.
 25. The method of claim 16, wherein the plurality ofintensity signals and the additional intensity signal each includes asignal portion and a noise portion, and wherein a non-zero referencesignal corresponds to the signal portion of one of the intensitysignals.
 26. The method of claim 16, wherein the pulsing blood comprisesarterial blood.
 27. The method of claim 16, wherein the pulsing bloodcomprises venous blood.
 28. A physiological monitor for determining aphysiological parameter of a patient, the physiological monitorcomprising: an input which receives three or more intensity signals fromat least one light-sensitive detector which detects light attenuated bybody tissue carrying pulsing blood, wherein the three or more intensitysignals correspond to detection of at least three wavelengths of thelight; and a processor which determines a value of oxygen saturationusing the three or more intensity signals, wherein the three or moreintensity signals include motion induced noise.
 29. The physiologicalmonitor of claim 28, wherein the processor processes at least two of thethree or more intensity signals with an adaptive algorithm.
 30. Thephysiological monitor of claim 29, wherein the adaptive algorithmcomprises a least squares algorithm.
 31. The physiological monitor ofclaim 30, wherein the least squares algorithm comprises a least squareslattice.
 32. The physiological monitor of claim 28, the processorprocesses at least two of the three or more intensity signals with aleast squares algorithm.
 33. The physiological monitor of claim 28,wherein one of the three or more intensity signals corresponds to one ofthe at least three wavelengths and wherein the processor uses the oneintensity signal primarily to reduce an effect of the motion inducednoise on the value of oxygen saturation.
 34. The physiological monitorof claim 33, wherein two of the three or more intensity signalscorresponds to two of the at least three wavelengths and wherein theprocessor uses the one intensity signal primarily to determine the valueof oxygen saturation.
 35. The physiological monitor of claim 28, whereinabsorption coefficients associated with two of the at least threewavelengths are related to one another.
 36. The physiological monitor ofclaim 35, wherein absorption coefficients associated with two of the atleast three wavelengths are proportional to one another.
 37. Thephysiological monitor of claim 35, wherein absorption coefficientsassociated with two of the at least three wavelengths are linearlyproportional to one another.
 38. The physiological monitor of claim 28,wherein absorption coefficients associated with the at least threewavelengths are proportional to one another.
 39. The physiologicalmonitor of claim 28, wherein each of the three or more intensity signalsincludes a signal portion and a noise portion, and wherein a non-zeroreference signal corresponds to the noise portion of one of the three ormore intensity signals.
 40. The physiological monitor of claim 28,wherein each of the three or more intensity signals includes a signalportion and a noise portion, and wherein a non-zero reference signalcorresponds to the signal portion of one of the three or more intensitysignals.
 41. The physiological monitor of claim 28, wherein the pulsingblood comprises arterial blood.
 42. The physiological monitor of claim28, wherein the pulsing blood comprises venous blood.